Question 1

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so.
-$5 x-y=22$
$3 x+y=18$

Accepted Answer

A)  $\{(3,5)\}$ 
B)  $\{(5,3)\}$ 
C)  $\{(5,4)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(3,5)\}$ 
B)  $\{(5,3)\}$ 
C)  $\{(5,4)\}$ 
D)  $\varnothing$; inconsistent system

Question 2

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so.
-$9 x+9 y=18$
$6 x-7 y=12$

Accepted Answer

A)  $\{(2,0)\}$ 
B)  $\{(2,1)\}$ 
C)  $\{(1,1)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(2,0)\}$ 
B)  $\{(2,1)\}$ 
C)  $\{(1,1)\}$ 
D)  $\varnothing$; inconsistent system

Question 3

Decide whether the ordered pair is a solution of the given system
-$4 x+y=-21$
$2 x+4 y=-14 ;(-5,1)$

Accepted Answer

A) True 
 B)False

Question 4

Without solving the following system of equations, tell what the solution is. Explain your answer.
$6 x+3 y+5 z=6$
$18 x+9 y+15 z=4$
$-24 x-12 y-20 z=5$

Accepted Answer

There are no solutions since t

Question 5

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $4 \%$ cement should he mix with 3 bags of $44 \%$ cement to produce a mix containing $12 \%$ cement?

Accepted Answer

A)  14 bags 
B)  15 bags 
C)  12 bags 
D)  20 bags 
A)  14 bags 
B)  15 bags 
C)  12 bags 
D)  20 bags

Question 6

Solve the system. Express the solution in the form $(x, y, z, w)$.
-$\begin{aligned}
4 y+w & =-19 \
X+y+2 z-w & =9 \
4 x+z+2 w & =13 \
X+y+2 z & =6
\end{aligned}$

Accepted Answer

A)  $\{(4,-16,6,-6)\}$ 
B)  $\{(4,-4,3,-3)\}$ 
C)  $\{(16,-16,6,-12)\}$ 
D)  $\{(4,-4,6,-3)\}$ 
A)  $\{(4,-16,6,-6)\}$ 
B)  $\{(4,-4,3,-3)\}$ 
C)  $\{(16,-16,6,-12)\}$ 
D)  $\{(4,-4,6,-3)\}$

Question 7

$2.4 x+3.5 y-1.7 z=24.72$ 
$0.3 x-1.7 y+5.1 z=-26.60$
$5.1 x-2.7 y-8.5 z=35.06$

Accepted Answer

A)  $\{(2.0,3.7,-4.1)\}$ 
B)  $\{(4,3.7,-12.3)\}$ 
C)  $\{(2.0,-3.7,-4.1)\}$ 
D)  $\{(2.0,3.7,4.1)\}$ 
A)  $\{(2.0,3.7,-4.1)\}$ 
B)  $\{(4,3.7,-12.3)\}$ 
C)  $\{(2.0,-3.7,-4.1)\}$ 
D)  $\{(2.0,3.7,4.1)\}$

Question 8

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $\$ 236,000$. How many people paid $\$ 12.00$ for reserved seats, and how many paid $\$ 4.00$ for general admission?

Accepted Answer

A)  Reserved: 11,000 ; general admission: 24,000 
B)  Reserved: 12,000 ; general admission: 23,000 
C)  Reserved: 23,000 ; general admission: 12,000 
D)  Reserved: 24,000 ; general admission: 11,000 
A)  Reserved: 11,000 ; general admission: 24,000 
B)  Reserved: 12,000 ; general admission: 23,000 
C)  Reserved: 23,000 ; general admission: 12,000 
D)  Reserved: 24,000 ; general admission: 11,000

Question 9

A company manufactures three products. The graph shows the production from 1986 to 1996. Which of the companies experience production decline over the period shown in the graph?

Accepted Answer

A)  Company A and Company C 
B)  Company A 
C)  Company C 
D)  Company B and Company C 
A)  Company A and Company C 
B)  Company A 
C)  Company C 
D)  Company B and Company C

Question 10

Solve by any method. Assume $a$ and $b$ represent nonzero constants.
-$\mathrm{ax}+\mathrm{by}=2$
$2 \mathrm{ax}+4 \mathrm{by}=1$

Accepted Answer

A)  $\left\{\left\{\frac{7 b}{2},-\frac{3 a}{2}\right)\right\}$ 
B)  $\left\{\left\{-\frac{3}{2 b}, \frac{7}{2 a}\right)\right\}$ 
C)  $\left\{\left\{\left(\frac{7 a}{2},-\frac{3}{2 b}\right)\right\}\right.$ 
D)  $\left\{\left\{\left(\frac{7}{2 a},-\frac{3}{2 b}\right)\right\}\right.$ 
A)  $\left\{\left\{\frac{7 b}{2},-\frac{3 a}{2}\right)\right\}$ 
B)  $\left\{\left\{-\frac{3}{2 b}, \frac{7}{2 a}\right)\right\}$ 
C)  $\left\{\left\{\left(\frac{7 a}{2},-\frac{3}{2 b}\right)\right\}\right.$ 
D)  $\left\{\left\{\left(\frac{7}{2 a},-\frac{3}{2 b}\right)\right\}\right.$

Question 11

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
-$5 x-2 y=3$
$-20 x+8 y=-12$

Accepted Answer

A)  $\{(-3,-9)\}$ 
B)  $\{(1,1)\}$ 
C)  $\{(x, y) \mid 5 x-2 y=3\}$; dependent equations 
D)  $\varnothing$; inconsistent system 
A)  $\{(-3,-9)\}$ 
B)  $\{(1,1)\}$ 
C)  $\{(x, y) \mid 5 x-2 y=3\}$; dependent equations 
D)  $\varnothing$; inconsistent system

Question 12

Solve the system. Express the solution in the form $(x, y, z, w)$.
-$2 x+2 y-6 z+w=-27$
$-x+y+2 z-w=4$
$2 x-y+z+2 w=9$
$\mathrm{x}+\mathrm{y}+2 \mathrm{z}-\mathrm{w}=8$

Accepted Answer

A)  $\{(2,-6,-4,-1)\}$ 
B)  $\{(-2,-3,4,-2)\}$ 
C)  $\{(4,-1,2,-2)\}$ 
D)  $\{(2,-3,4,-1)\}$ 
A)  $\{(2,-6,-4,-1)\}$ 
B)  $\{(-2,-3,4,-2)\}$ 
C)  $\{(4,-1,2,-2)\}$ 
D)  $\{(2,-3,4,-1)\}$

Question 13

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
-$6 x+9 y=69$
$-2 x-3 y=-23$

Accepted Answer

A)  $\{(-3,10)\}$ 
B)  $\{(-2,9)\}$ 
C)  $\{(-2,10)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(-3,10)\}$ 
B)  $\{(-2,9)\}$ 
C)  $\{(-2,10)\}$ 
D)  $\varnothing$; inconsistent system

Question 14

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$\begin{aligned}
& x-y+2 z=11 \
& -2 x+2 y-4 z=3 \
& x+4 y+z=23
\end{aligned}$

Accepted Answer

A)  $\{(x, y, z) \mid x-y+2 z=11\}$; dependent equations 
B)  $\{(0,5,3)\}$ 
C)  $\{(3,0,5)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(x, y, z) \mid x-y+2 z=11\}$; dependent equations 
B)  $\{(0,5,3)\}$ 
C)  $\{(3,0,5)\}$ 
D)  $\varnothing$; inconsistent system

Question 15

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$4 x+4 y=28$
$4 x-2 y=16$

Accepted Answer

A)  $\{(2,5)\}$ 
B)  $\{(5,2)\}$ 
C)  $\{(4,0)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(2,5)\}$ 
B)  $\{(5,2)\}$ 
C)  $\{(4,0)\}$ 
D)  $\varnothing$; inconsistent system

Question 16

The table shown was generated by a graphing calculator. The functions defined by $y_{1}$ and y2 are linear. Based on the table, find the coordinates of the point of intersection of the graphs.

Accepted Answer

A)  $(7,7)$ 
B)  $(7,2)$ 
C)  $(3,9)$ 
D)  $(2,7)$ 
A)  $(7,7)$ 
B)  $(7,2)$ 
C)  $(3,9)$ 
D)  $(2,7)$

Question 17

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so.
-$\frac{1}{4} x+y=6$
$x-24=-4 y$

Accepted Answer

A)  $\{(4,5)\}$ 
B)  $\{(24,0)\}$ 
C)  $\{(x, y) \mid x+4 y=24\}$; dependent equations 
D)  $\varnothing$; inconsistent system 
A)  $\{(4,5)\}$ 
B)  $\{(24,0)\}$ 
C)  $\{(x, y) \mid x+4 y=24\}$; dependent equations 
D)  $\varnothing$; inconsistent system

Question 18

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 8 feet longer than the width and the perimeter is 116 feet. What is the width of the rectangle?

Accepted Answer

A)  50 feet 
B)  24 feet 
C)  27 feet 
D)  25 feet 
A)  50 feet 
B)  24 feet 
C)  27 feet 
D)  25 feet

Question 19

A merchant has coffee worth $\$ 40$ a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $\$ 70$ a pound. How many pounds (lb) of the $\$ 40$ coffee should be used?

Accepted Answer

A)  $20 \mathrm{lb}$ 
B)  $40 \mathrm{lb}$ 
C)  $80 \mathrm{lb}$ 
D)  $10 \mathrm{lb}$ 
A)  $20 \mathrm{lb}$ 
B)  $40 \mathrm{lb}$ 
C)  $80 \mathrm{lb}$ 
D)  $10 \mathrm{lb}$

Question 20

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$2 x-2 y+8 z=16$
$-5 x+5 y-20 z=-40$
$\mathrm{x}-\mathrm{y}+4 \mathrm{z}=8$

Accepted Answer

A)  $\{(x, y, z) \mid x-y+4 z=8\}$; dependent equations 
B)  $\varnothing$; inconsistent system 
C)  $\{(7,3,1)\}$ 
D)  $\{(0,0,2)\}$ 
A)  $\{(x, y, z) \mid x-y+4 z=8\}$; dependent equations 
B)  $\varnothing$; inconsistent system 
C)  $\{(7,3,1)\}$ 
D)  $\{(0,0,2)\}$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $5 x-y=22$ $3 x+y=18$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $9 x+9 y=18$ $6 x-7 y=12$

Decide whether the ordered pair is a solution of the given system - $4 x+y=-21$ $2 x+4 y=-14 ;(-5,1)$

Without solving the following system of equations, tell what the solution is. Explain your answer. $6 x+3 y+5 z=6$ $18 x+9 y+15 z=4$ $-24 x-12 y-20 z=5$

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $4 \%$ cement should he mix with 3 bags of $44 \%$ cement to produce a mix containing $12 \%$ cement?

Solve the system. Express the solution in the form $(x, y, z, w)$ . - 4y+w =-19 X+y+2z-w =9 4x+z+2w =13 X+y+2z =6

$2.4 x+3.5 y-1.7 z=24.72$ $0.3 x-1.7 y+5.1 z=-26.60$ $5.1 x-2.7 y-8.5 z=35.06$

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $\$ 236,000$ . How many people paid $\$ 12.00$ for reserved seats, and how many paid $\$ 4.00$ for general admission?

A company manufactures three products. The graph shows the production from 1986 to 1996. Which of the companies experience production decline over the period shown in the graph?

Solve by any method. Assume $a$ and $b$ represent nonzero constants. - $\mathrm{ax}+\mathrm{by}=2$ $2 \mathrm{ax}+4 \mathrm{by}=1$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $5 x-2 y=3$ $-20 x+8 y=-12$

Solve the system. Express the solution in the form $(x, y, z, w)$ . - $2 x+2 y-6 z+w=-27$ $-x+y+2 z-w=4$ $2 x-y+z+2 w=9$ $\mathrm{x}+\mathrm{y}+2 \mathrm{z}-\mathrm{w}=8$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $6 x+9 y=69$ $-2 x-3 y=-23$

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - x-y+2z=11 -2x+2y-4z=3 x+4y+z=23

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $4 x+4 y=28$ $4 x-2 y=16$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $\frac{1}{4} x+y=6$ $x-24=-4 y$

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 8 feet longer than the width and the perimeter is 116 feet. What is the width of the rectangle?

A merchant has coffee worth $\$ 40$ a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $\$ 70$ a pound. How many pounds (lb) of the $\$ 40$ coffee should be used?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $2 x-2 y+8 z=16$ $-5 x+5 y-20 z=-40$ $\mathrm{x}-\mathrm{y}+4 \mathrm{z}=8$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 4: Systems of Linear Equations

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - 5x−y=225 x-y=225x−y=22 3x+y=183 x+y=183x+y=18

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - 9x+9y=189 x+9 y=189x+9y=18 6x−7y=126 x-7 y=126x−7y=12

Decide whether the ordered pair is a solution of the given system - 4x+y=−214 x+y=-214x+y=−21 2x+4y=−14;(−5,1)2 x+4 y=-14 ;(-5,1)2x+4y=−14;(−5,1)

Without solving the following system of equations, tell what the solution is. Explain your answer. 6x+3y+5z=66 x+3 y+5 z=66x+3y+5z=6 18x+9y+15z=418 x+9 y+15 z=418x+9y+15z=4 −24x−12y−20z=5-24 x-12 y-20 z=5−24x−12y−20z=5

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 4%4 \%4% cement should he mix with 3 bags of 44%44 \%44% cement to produce a mix containing 12%12 \%12% cement?

Solve the system. Express the solution in the form (x,y,z,w)(x, y, z, w)(x,y,z,w) . - 4y+w =-19 X+y+2z-w =9 4x+z+2w =13 X+y+2z =6

2.4x+3.5y−1.7z=24.722.4 x+3.5 y-1.7 z=24.722.4x+3.5y−1.7z=24.72 0.3x−1.7y+5.1z=−26.600.3 x-1.7 y+5.1 z=-26.600.3x−1.7y+5.1z=−26.60 5.1x−2.7y−8.5z=35.065.1 x-2.7 y-8.5 z=35.065.1x−2.7y−8.5z=35.06

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $236,000\$ 236,000$236,000 . How many people paid $12.00\$ 12.00$12.00 for reserved seats, and how many paid $4.00\$ 4.00$4.00 for general admission?

A company manufactures three products. The graph shows the production from 1986 to 1996. Which of the companies experience production decline over the period shown in the graph?

Solve by any method. Assume aaa and bbb represent nonzero constants. - ax+by=2\mathrm{ax}+\mathrm{by}=2ax+by=2 2ax+4by=12 \mathrm{ax}+4 \mathrm{by}=12ax+4by=1

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - 5x−2y=35 x-2 y=35x−2y=3 −20x+8y=−12-20 x+8 y=-12−20x+8y=−12

Solve the system. Express the solution in the form (x,y,z,w)(x, y, z, w)(x,y,z,w) . - 2x+2y−6z+w=−272 x+2 y-6 z+w=-272x+2y−6z+w=−27 −x+y+2z−w=4-x+y+2 z-w=4−x+y+2z−w=4 2x−y+z+2w=92 x-y+z+2 w=92x−y+z+2w=9 x+y+2z−w=8\mathrm{x}+\mathrm{y}+2 \mathrm{z}-\mathrm{w}=8x+y+2z−w=8

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - 6x+9y=696 x+9 y=696x+9y=69 −2x−3y=−23-2 x-3 y=-23−2x−3y=−23

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - x-y+2z=11 -2x+2y-4z=3 x+4y+z=23

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - 4x+4y=284 x+4 y=284x+4y=28 4x−2y=164 x-2 y=164x−2y=16

The table shown was generated by a graphing calculator. The functions defined by y1y_{1}y1​ and y2 are linear. Based on the table, find the coordinates of the point of intersection of the graphs.

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - 14x+y=6\frac{1}{4} x+y=641​x+y=6 x−24=−4yx-24=-4 yx−24=−4y

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 8 feet longer than the width and the perimeter is 116 feet. What is the width of the rectangle?

A merchant has coffee worth $40\$ 40$40 a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $70\$ 70$70 a pound. How many pounds (lb) of the $40\$ 40$40 coffee should be used?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - 2x−2y+8z=162 x-2 y+8 z=162x−2y+8z=16 −5x+5y−20z=−40-5 x+5 y-20 z=-40−5x+5y−20z=−40 x−y+4z=8\mathrm{x}-\mathrm{y}+4 \mathrm{z}=8x−y+4z=8

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $5 x-y=22$ $3 x+y=18$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $9 x+9 y=18$ $6 x-7 y=12$

Decide whether the ordered pair is a solution of the given system - $4 x+y=-21$ $2 x+4 y=-14 ;(-5,1)$

Without solving the following system of equations, tell what the solution is. Explain your answer. $6 x+3 y+5 z=6$ $18 x+9 y+15 z=4$ $-24 x-12 y-20 z=5$

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $4 \%$ cement should he mix with 3 bags of $44 \%$ cement to produce a mix containing $12 \%$ cement?

Solve the system. Express the solution in the form $(x, y, z, w)$ . - 4y+w =-19 X+y+2z-w =9 4x+z+2w =13 X+y+2z =6

$2.4 x+3.5 y-1.7 z=24.72$ $0.3 x-1.7 y+5.1 z=-26.60$ $5.1 x-2.7 y-8.5 z=35.06$

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $\$ 236,000$ . How many people paid $\$ 12.00$ for reserved seats, and how many paid $\$ 4.00$ for general admission?

Solve by any method. Assume $a$ and $b$ represent nonzero constants. - $\mathrm{ax}+\mathrm{by}=2$ $2 \mathrm{ax}+4 \mathrm{by}=1$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $5 x-2 y=3$ $-20 x+8 y=-12$

Solve the system. Express the solution in the form $(x, y, z, w)$ . - $2 x+2 y-6 z+w=-27$ $-x+y+2 z-w=4$ $2 x-y+z+2 w=9$ $\mathrm{x}+\mathrm{y}+2 \mathrm{z}-\mathrm{w}=8$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $6 x+9 y=69$ $-2 x-3 y=-23$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $4 x+4 y=28$ $4 x-2 y=16$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $\frac{1}{4} x+y=6$ $x-24=-4 y$

A merchant has coffee worth $\$ 40$ a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $\$ 70$ a pound. How many pounds (lb) of the $\$ 40$ coffee should be used?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $2 x-2 y+8 z=16$ $-5 x+5 y-20 z=-40$ $\mathrm{x}-\mathrm{y}+4 \mathrm{z}=8$