Question 1

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$x+y=-8$
$8 x-y=-64$

Accepted Answer

A)  $\{(-8,0)\}$ 
B)  $\{(-8,8)\}$ 
C)  $\{(0,-8)\}$ 
D)  $\{(0,8)\}$ 
A)  $\{(-8,0)\}$ 
B)  $\{(-8,8)\}$ 
C)  $\{(0,-8)\}$ 
D)  $\{(0,8)\}$

Question 2

During the 1998-1999 Little League season, the Tigers played 50 games. They won 6 more games than they lost. How many games did they lose that season?

Accepted Answer

A)  22 games 
B)  20 games 
C)  25 games 
D)  28 games 
A)  22 games 
B)  20 games 
C)  25 games 
D)  28 games

Question 3

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$3 x-9 y+8 z=-30$
$-12 x+36 y-32 z=120$
$15 x-45 y+40 z=-150$

Accepted Answer

A)  $\{(x, y, z) \mid 3 x-9 y+8 z=-30\}$; dependent equations 
B)  $\{(-8,-2,-3)\}$ 
C)  $\varnothing$; inconsistent system 
D)  $\{(8,2,3)\}$ 
A)  $\{(x, y, z) \mid 3 x-9 y+8 z=-30\}$; dependent equations 
B)  $\{(-8,-2,-3)\}$ 
C)  $\varnothing$; inconsistent system 
D)  $\{(8,2,3)\}$

Question 4

Tell how many solutions the system has. Do not actually solve.
-$x-2 y=5$
$2 x-4 y=18$

Accepted Answer

A)  No solution 
B)  One solution 
C)  Infinitely many 
A)  No solution 
B)  One solution 
C)  Infinitely many

Question 5

$7 x+7 y+z=1$
$x+8 y+8 z=8$
$9 \mathrm{x}+\mathrm{y}+9 \mathrm{z}=9$

Accepted Answer

A)  $\{(0,1,0)\}$ 
B)  $\{(0,0,1)\}$ 
C)  $\{(-1,1,1)\}$ 
D)  $\{(1,-1,1)\}$ 
A)  $\{(0,1,0)\}$ 
B)  $\{(0,0,1)\}$ 
C)  $\{(-1,1,1)\}$ 
D)  $\{(1,-1,1)\}$

Question 6

The perimeter of a triangle is 29 inches. Three times the length of the longest side minus the length of the shortest side is 53 inches. The sum of the length of the longest side and three times the sum of both the other side lengths is 49 inches. Find the side lengths.

Accepted Answer

A)  4 in., 6 in., 19 in. 
B)  4 in., 7 in., 18 in. 
C)  3 in., 6 in., 20 in. 
D)  No solution 
A)  4 in., 6 in., 19 in. 
B)  4 in., 7 in., 18 in. 
C)  3 in., 6 in., 20 in. 
D)  No solution

Question 7

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
-$x+4 y=13$
$2 x+3 y=6$

Accepted Answer

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

Question 8

The solution set of the system $y_{1}=2 x+3$ and $y_{2}=-x+9$ is $\{(2,7)\}$. Using slopes and $y$-intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Accepted Answer

A)  Neither is correct. 
B)  Right 
C)  Left 
D)  Both could be correct. 
A)  Neither is correct. 
B)  Right 
C)  Left 
D)  Both could be correct.

Question 9

The perimeter of a rectangle is $60 \mathrm{~m}$. If the width were doubled and the length were increased by 15 $\mathrm{m}$, the perimeter would be $108 \mathrm{~m}$. What are the length and width of the rectangle?

Accepted Answer

A)  Length: $15 \mathrm{~m}$; width: $15 \mathrm{~m}$ 
B)  Length: $15 \mathrm{~m}$; width: $10 \mathrm{~m}$ 
C)  Length: $21 \mathrm{~m}$; width: $9 \mathrm{~m}$ 
D)  Length: $9 \mathrm{~m}$; width: $21 \mathrm{~m}$ 
A)  Length: $15 \mathrm{~m}$; width: $15 \mathrm{~m}$ 
B)  Length: $15 \mathrm{~m}$; width: $10 \mathrm{~m}$ 
C)  Length: $21 \mathrm{~m}$; width: $9 \mathrm{~m}$ 
D)  Length: $9 \mathrm{~m}$; width: $21 \mathrm{~m}$

Question 10

Solve the system of equations.
-$\frac{4}{y}+\frac{2}{x}=-\frac{1}{2}$
$\frac{5}{y}+\frac{4}{x}=-\frac{1}{4}$

Accepted Answer

A)  $\left\{\left\{\left(\frac{1}{4},-\frac{1}{4}\right)\right\}\right.$ 
B)  $\varnothing$ 
C)  $\{(4,4\})$ 
D)  $\{(4,-4\})$ 
A)  $\left\{\left\{\left(\frac{1}{4},-\frac{1}{4}\right)\right\}\right.$ 
B)  $\varnothing$ 
C)  $\{(4,4\})$ 
D)  $\{(4,-4\})$

Question 11

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$x+y=-1$
$x+y=-6$

Accepted Answer

A)  $\{(0,-7)\}$ 
B)  $\varnothing$; inconsistent system 
C)  $\{(-1,-6)\}$ 
D)  $\{(x, y) \mid x+y=-6\}$; dependent equations 
A)  $\{(0,-7)\}$ 
B)  $\varnothing$; inconsistent system 
C)  $\{(-1,-6)\}$ 
D)  $\{(x, y) \mid x+y=-6\}$; dependent equations

Question 12

The side of an equilateral triangle is 7 inches shorter than the side of a square. The perimeter of the square is 43 inches more than the perimeter of the triangle. Find the length of a side of the triangle.

Accepted Answer

A)  22 inches 
B)  24 inches 
C)  15 inches 
D)  21 inches 
A)  22 inches 
B)  24 inches 
C)  15 inches 
D)  21 inches

Question 13

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$x+\frac{1}{2} y-\frac{1}{2} z=3$
$4 x+2 y-2 z=12$
$-2 \mathrm{x}-\mathrm{y}+\mathrm{z}=-6$

Accepted Answer

A)  $\{(3,1,1)\}$ 
B)  $\varnothing$; inconsistent system 
C)  $\{(x, y, z) \mid-2 x-y+z=-6\}$; dependent equations 
D)  $\{(3,0,0)\}$ 
A)  $\{(3,1,1)\}$ 
B)  $\varnothing$; inconsistent system 
C)  $\{(x, y, z) \mid-2 x-y+z=-6\}$; dependent equations 
D)  $\{(3,0,0)\}$

Question 14

Graphs of two linear functions $f$ and $g$ that are neither parallel nor coincident intersect in how many points?

Accepted Answer

A)  None 
B)  Two 
C)  One 
D)  Infinitely many points 
A)  None 
B)  Two 
C)  One 
D)  Infinitely many points

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response
-Give the definition or an example of the word or phrase.
Dependent system

Accepted Answer

A system having infi

Question 16

Solve by any method. Assume $a$ and $b$ represent nonzero constants.
-$a x+b y=1$
Ax - by $=14$

Accepted Answer

A)  $\left\{\left(\frac{15}{2 a},-\frac{13}{2 b}\right)\right\}$ 
B)  $\left\{\left\{\frac{13}{a},-\frac{15}{2 b}\right)\right\}$ 
C)  $\left\{\left(\frac{15}{2 a}, \frac{13}{2 b}\right)\right\}$ 
D)  $\left\{\left(-\frac{15}{2 a},-\frac{13}{2 b}\right)\right\}$ 
A)  $\left\{\left(\frac{15}{2 a},-\frac{13}{2 b}\right)\right\}$ 
B)  $\left\{\left\{\frac{13}{a},-\frac{15}{2 b}\right)\right\}$ 
C)  $\left\{\left(\frac{15}{2 a}, \frac{13}{2 b}\right)\right\}$ 
D)  $\left\{\left(-\frac{15}{2 a},-\frac{13}{2 b}\right)\right\}$

Question 17

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 equation for $\mathrm{y}_{2}$.

Accepted Answer

A)  $y_{2}=-x+3$ 
B)  $y_{2}=2 x+9$ 
C)  $y 2=2 x+3$ 
D)  $y_{2}=-x+9$ 
A)  $y_{2}=-x+3$ 
B)  $y_{2}=2 x+9$ 
C)  $y 2=2 x+3$ 
D)  $y_{2}=-x+9$

Question 18

After retirement, Kelly's company offers her two options for receiving her retirement pension. According the the first plan, she will receive monthly payments from a variable annuity that initially pays $\$ 700$ per month then decreases each month at a rate of $\$ 25$ per month per year. Optionally, she may choose a plan that pays her a fixed amount of $\$ 500$ per month for the rest of her life. The monthly payments for the two plans are illustrated in the graph below. After how many years does the variable plan pay less per month than the fixed plan?

Accepted Answer

A)  Up to 8 years 
B)  8 years 
C)  9 years 
D)  The variable plan always pays less. 
A)  Up to 8 years 
B)  8 years 
C)  9 years 
D)  The variable plan always pays less.

Question 19

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
-$-x+6 y=9$
$8 x-6 y=54$

Accepted Answer

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

Question 20

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$5 x-2 y=-1$
$x+4 y=35$

Accepted Answer

A)  $\{(3,8)\}$ 
B)  $\{(2,8)\}$ 
C)  $\{(2,9)\}$ 
D)  $\{(3,9)\}$ 
A)  $\{(3,8)\}$ 
B)  $\{(2,8)\}$ 
C)  $\{(2,9)\}$ 
D)  $\{(3,9)\}$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x+y=-8$ $8 x-y=-64$

During the 1998-1999 Little League season, the Tigers played 50 games. They won 6 more games than they lost. How many games did they lose that season?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $3 x-9 y+8 z=-30$ $-12 x+36 y-32 z=120$ $15 x-45 y+40 z=-150$

Tell how many solutions the system has. Do not actually solve. - $x-2 y=5$ $2 x-4 y=18$

$7 x+7 y+z=1$ $x+8 y+8 z=8$ $9 \mathrm{x}+\mathrm{y}+9 \mathrm{z}=9$

The perimeter of a triangle is 29 inches. Three times the length of the longest side minus the length of the shortest side is 53 inches. The sum of the length of the longest side and three times the sum of both the other side lengths is 49 inches. Find the side lengths.

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $x+4 y=13$ $2 x+3 y=6$

The perimeter of a rectangle is $60 \mathrm{~m}$ . If the width were doubled and the length were increased by 15 $\mathrm{m}$ , the perimeter would be $108 \mathrm{~m}$ . What are the length and width of the rectangle?

Solve the system of equations. - $\frac{4}{y}+\frac{2}{x}=-\frac{1}{2}$ $\frac{5}{y}+\frac{4}{x}=-\frac{1}{4}$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x+y=-1$ $x+y=-6$

The side of an equilateral triangle is 7 inches shorter than the side of a square. The perimeter of the square is 43 inches more than the perimeter of the triangle. Find the length of a side of the triangle.

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $x+\frac{1}{2} y-\frac{1}{2} z=3$ $4 x+2 y-2 z=12$ $-2 \mathrm{x}-\mathrm{y}+\mathrm{z}=-6$

Graphs of two linear functions $f$ and $g$ that are neither parallel nor coincident intersect in how many points?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response -Give the definition or an example of the word or phrase. Dependent system

Solve by any method. Assume $a$ and $b$ represent nonzero constants. - $a x+b y=1$ Ax - by $=14$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $-x+6 y=9$ $8 x-6 y=54$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $5 x-2 y=-1$ $x+4 y=35$

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. If the system is inconsistent or has dependent equations, say so. - x+y=−8x+y=-8x+y=−8 8x−y=−648 x-y=-648x−y=−64

During the 1998-1999 Little League season, the Tigers played 50 games. They won 6 more games than they lost. How many games did they lose that season?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - 3x−9y+8z=−303 x-9 y+8 z=-303x−9y+8z=−30 −12x+36y−32z=120-12 x+36 y-32 z=120−12x+36y−32z=120 15x−45y+40z=−15015 x-45 y+40 z=-15015x−45y+40z=−150

Tell how many solutions the system has. Do not actually solve. - x−2y=5x-2 y=5x−2y=5 2x−4y=182 x-4 y=182x−4y=18

7x+7y+z=17 x+7 y+z=17x+7y+z=1 x+8y+8z=8x+8 y+8 z=8x+8y+8z=8 9x+y+9z=99 \mathrm{x}+\mathrm{y}+9 \mathrm{z}=99x+y+9z=9

The perimeter of a triangle is 29 inches. Three times the length of the longest side minus the length of the shortest side is 53 inches. The sum of the length of the longest side and three times the sum of both the other side lengths is 49 inches. Find the side lengths.

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - x+4y=13x+4 y=13x+4y=13 2x+3y=62 x+3 y=62x+3y=6

The solution set of the system y1=2x+3y_{1}=2 x+3y1​=2x+3 and y2=−x+9y_{2}=-x+9y2​=−x+9 is {(2,7)}\{(2,7)\}{(2,7)} . Using slopes and yyy -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

The perimeter of a rectangle is 60 m60 \mathrm{~m}60 m . If the width were doubled and the length were increased by 15 m\mathrm{m}m , the perimeter would be 108 m108 \mathrm{~m}108 m . What are the length and width of the rectangle?

Solve the system of equations. - 4y+2x=−12\frac{4}{y}+\frac{2}{x}=-\frac{1}{2}y4​+x2​=−21​ 5y+4x=−14\frac{5}{y}+\frac{4}{x}=-\frac{1}{4}y5​+x4​=−41​

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - x+y=−1x+y=-1x+y=−1 x+y=−6x+y=-6x+y=−6

The side of an equilateral triangle is 7 inches shorter than the side of a square. The perimeter of the square is 43 inches more than the perimeter of the triangle. Find the length of a side of the triangle.

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - x+12y−12z=3x+\frac{1}{2} y-\frac{1}{2} z=3x+21​y−21​z=3 4x+2y−2z=124 x+2 y-2 z=124x+2y−2z=12 −2x−y+z=−6-2 \mathrm{x}-\mathrm{y}+\mathrm{z}=-6−2x−y+z=−6

Graphs of two linear functions fff and ggg that are neither parallel nor coincident intersect in how many points?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response -Give the definition or an example of the word or phrase. Dependent system

Solve by any method. Assume aaa and bbb represent nonzero constants. - ax+by=1a x+b y=1ax+by=1 Ax - by =14=14=14

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 equation for y2\mathrm{y}_{2}y2​ .

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - −x+6y=9-x+6 y=9−x+6y=9 8x−6y=548 x-6 y=548x−6y=54

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - 5x−2y=−15 x-2 y=-15x−2y=−1 x+4y=35x+4 y=35x+4y=35

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. If the system is inconsistent or has dependent equations, say so. - $x+y=-8$ $8 x-y=-64$

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $3 x-9 y+8 z=-30$ $-12 x+36 y-32 z=120$ $15 x-45 y+40 z=-150$

Tell how many solutions the system has. Do not actually solve. - $x-2 y=5$ $2 x-4 y=18$

$7 x+7 y+z=1$ $x+8 y+8 z=8$ $9 \mathrm{x}+\mathrm{y}+9 \mathrm{z}=9$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $x+4 y=13$ $2 x+3 y=6$

The perimeter of a rectangle is $60 \mathrm{~m}$ . If the width were doubled and the length were increased by 15 $\mathrm{m}$ , the perimeter would be $108 \mathrm{~m}$ . What are the length and width of the rectangle?

Solve the system of equations. - $\frac{4}{y}+\frac{2}{x}=-\frac{1}{2}$ $\frac{5}{y}+\frac{4}{x}=-\frac{1}{4}$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x+y=-1$ $x+y=-6$

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $x+\frac{1}{2} y-\frac{1}{2} z=3$ $4 x+2 y-2 z=12$ $-2 \mathrm{x}-\mathrm{y}+\mathrm{z}=-6$

Graphs of two linear functions $f$ and $g$ that are neither parallel nor coincident intersect in how many points?

Solve by any method. Assume $a$ and $b$ represent nonzero constants. - $a x+b y=1$ Ax - by $=14$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $-x+6 y=9$ $8 x-6 y=54$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $5 x-2 y=-1$ $x+4 y=35$