Question 1

Fill in the blank with one of the words or phrases listed below.
system of linear equations solution consistent independent
dependent inconsistent substitution addition
-In a system of linear equations in two variables, if the graphs of the equations are the same, the equations are_____________ equations.

Accepted Answer

A) inconsistent 
B) dependent 
C) independent 
D) addition

Question 2

Decide whether or not the ordered pair satisfies the system of linear equations.
-(-6, 5); $\left\{ \begin{array} { l } 
x + y = - 1 \
x - y = - 11
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 3

Without graphing, decide:
(a)Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point?
(b)How many solutions does the system have?
-$\left\{ \begin{aligned}
3 x - y & = 1 \
x + 4 y & = 22
\end{aligned} \right.$

Accepted Answer

A) lines intersecting at a single point; one solution 
B) parallel lines; no solution 
C) identical lines; infinite number of solutions

Question 4

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { r r } 
7 x + 2 y = & 9 \
- 2 x - 2 y = & - 24
\end{array} \right.$

Accepted Answer

A) (2, -15) 
B) (-3, 15) 
C) (7, -15) 
D) infinite number of solutions

Question 5

Solve the system by the substitution or the addition method.
-$\left\{ \begin{array} { l } 
x + \frac { 1 } { 51 } y = 3 \
- 3 x + 2 y = 12
\end{array} \right.$

Accepted Answer

A)  $\left( 2 \frac { 4 } { 5 } , 10 \frac { 1 } { 5 } \right)$ 
B)  $\left( 4 \frac { 4 } { 5 } , 8 \frac { 1 } { 5 } \right)$ 
C) (2, -3) 
D)  $\left( \frac { 1 } { 51 } , 1 \right)$

Question 6

Decide whether or not the ordered pair satisfies the system of linear equations.
-(2, -6); $\left\{ \begin{array} { l } 
4 x + y = 2 \
2 x + 4 y = - 20
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 7

Is the ordered pair a solution of the linear system?
-$\left\{ \begin{array} { l } 
5 x - 3 y = 21 \
4 x + 5 y = - 3
\end{array} ; \quad ( 3 , - 2 ) \right.$

Accepted Answer

A) True 
 B)False

Question 8

Decide whether or not the ordered pair satisfies the system of linear equations.
-(3, -1); $\left\{ \begin{array} { l } 
x + y = - 4 \
x - y = - 2
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 9

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
3 x - 5 y = - 7 \
3 x - 5 y = 8
\end{array} \right.$

Accepted Answer

A) (-7, 8) 
B)  $\left( - \frac { 7 } { 5 } , \frac { 8 } { 3 } \right)$ 
C) (3, 5) 
D) no solution

Question 10

Solve the system of equations by graphing the equations on the same set of axes.
-$$\left\{ \begin{array} { l } 
x + y = 1 \
x - y = 5
\end{array} \right.$$

Accepted Answer

A) (3, 2) 
B) (-2, 3) 
C) (3, -2) 
D) no solution

Question 11

Answer true or false.
-If the two equations in a system of linear equations are added and the result is 8 = 0, the system has no solution.

Accepted Answer

A) True 
 B)False

Question 12

Answer true or false.
-Although (7, 3)is not a solution of x + 3y = 2, it can still be a solution of the system $\left\{ \begin{array} { l } 
x + 3 y = 2 \
x + y = 4
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 13

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
3 x - 5 y = 3 \
2 x - 3 y = 3
\end{array} \right.$

Accepted Answer

A) (6, 3) 
B) (3, 6) 
C) infinite number of solutions 
D) no solution

Question 14

Is the ordered pair a solution of the linear system?
-$\left\{ \begin{array} { l } 
2 x - 4 y = 6 \
5 x + y = 1
\end{array} ; ( 1 , - 1 ) \right.$

Accepted Answer

A) True 
 B)False

Question 15

Solve the problem.
-The three angles in a triangle always add up to 180°. If one angle in a triangle is 114° and the second is 5 times the third, what are the three angles?

Accepted Answer

A) 114°, 54°, 12° 
B) 114°, 53°, 13° 
C) 114°, 56°, 10° 
D) 114°, 55°, 11°

Question 16

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { r } 
x + 8 y = - 39 \
2 x + 8 y = - 46
\end{array} \right.$

Accepted Answer

A) (4, -7) 
B) (-7, -4) 
C) infinite number of solutions 
D) no solution

Question 17

Solve the problem.
-Julie and Eric row their boat (at a constant speed)35 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of the current.

Accepted Answer

A) 2 mph 
B) 0.5 mph 
C) 1 mph 
D) 6 mph

Question 18

Answer true or false.
-If the two equations in a system of linear equations are added and the result is 7x = 0, the system has no
solution.

Accepted Answer

A) True 
 B)False

Question 19

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
x + y = 33 \
x - y = 13
\end{array} \right.$

Accepted Answer

A) No solution 
B) (10, 23) 
C)  $\left( \frac { 33 } { 2 } , \frac { 13 } { 2 } \right)$ 
D) (23, 10)

Question 20

Write a system of equations to describe the situation. Do not solve the system.
-One number is 5 more than another number. If you add 9 to 2 times the first number, the result is 3 times the second number.

Accepted Answer

A)  $\left\{ \begin{array} { l } 
x - y = 5 \
2 x - 3 y = - 9
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
x - y = 5 \
2 x - 3 y = 9
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x - y = 5 \
- 2 x + 3 y = - 9
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
x + y = 5 \
2 x - 3 y = - 9
\end{array} \right.$

Exam 11: Systems of Equations

Decide whether or not the ordered pair satisfies the system of linear equations. -(-6, 5); $\left\{ \begin{array} { l } x + y = - 1 \\x - y = - 11\end{array} \right.$

Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? - $\left\{ \begin{aligned}3 x - y & = 1 \\x + 4 y & = 22\end{aligned} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r r } 7 x + 2 y = & 9 \\- 2 x - 2 y = & - 24\end{array} \right.$

Solve the system by the substitution or the addition method. - $\left\{ \begin{array} { l } x + \frac { 1 } { 51 } y = 3 \\- 3 x + 2 y = 12\end{array} \right.$

Decide whether or not the ordered pair satisfies the system of linear equations. -(2, -6); $\left\{ \begin{array} { l } 4 x + y = 2 \\2 x + 4 y = - 20\end{array} \right.$

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 5 x - 3 y = 21 \\4 x + 5 y = - 3\end{array} ; \quad ( 3 , - 2 ) \right.$

Decide whether or not the ordered pair satisfies the system of linear equations. -(3, -1); $\left\{ \begin{array} { l } x + y = - 4 \\x - y = - 2\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 3 x - 5 y = - 7 \\3 x - 5 y = 8\end{array} \right.$

Answer true or false. -If the two equations in a system of linear equations are added and the result is 8 = 0, the system has no solution.

Answer true or false. -Although (7, 3)is not a solution of x + 3y = 2, it can still be a solution of the system $\left\{ \begin{array} { l } x + 3 y = 2 \\x + y = 4\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 3 x - 5 y = 3 \\2 x - 3 y = 3\end{array} \right.$

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 2 x - 4 y = 6 \\5 x + y = 1\end{array} ; ( 1 , - 1 ) \right.$

Solve the problem. -The three angles in a triangle always add up to 180°. If one angle in a triangle is 114° and the second is 5 times the third, what are the three angles?

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r } x + 8 y = - 39 \\2 x + 8 y = - 46\end{array} \right.$

Solve the problem. -Julie and Eric row their boat (at a constant speed) 35 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of the current.

Answer true or false. -If the two equations in a system of linear equations are added and the result is 7x = 0, the system has no solution.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 33 \\x - y = 13\end{array} \right.$

Write a system of equations to describe the situation. Do not solve the system. -One number is 5 more than another number. If you add 9 to 2 times the first number, the result is 3 times the second number.

Exam 11: Systems of Equations

Decide whether or not the ordered pair satisfies the system of linear equations. -(-6, 5); {x+y=−1x−y=−11\left\{ \begin{array} { l } x + y = - 1 \\x - y = - 11\end{array} \right.{x+y=−1x−y=−11​

Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? - {3x−y=1x+4y=22\left\{ \begin{aligned}3 x - y & = 1 \\x + 4 y & = 22\end{aligned} \right.{3x−yx+4y​=1=22​

Solve the system of equations by the addition method. - {7x+2y=9−2x−2y=−24\left\{ \begin{array} { r r } 7 x + 2 y = & 9 \\- 2 x - 2 y = & - 24\end{array} \right.{7x+2y=−2x−2y=​9−24​

Solve the system by the substitution or the addition method. - {x+151y=3−3x+2y=12\left\{ \begin{array} { l } x + \frac { 1 } { 51 } y = 3 \\- 3 x + 2 y = 12\end{array} \right.{x+511​y=3−3x+2y=12​

Decide whether or not the ordered pair satisfies the system of linear equations. -(2, -6); {4x+y=22x+4y=−20\left\{ \begin{array} { l } 4 x + y = 2 \\2 x + 4 y = - 20\end{array} \right.{4x+y=22x+4y=−20​

Is the ordered pair a solution of the linear system? - {5x−3y=214x+5y=−3;(3,−2)\left\{ \begin{array} { l } 5 x - 3 y = 21 \\4 x + 5 y = - 3\end{array} ; \quad ( 3 , - 2 ) \right.{5x−3y=214x+5y=−3​;(3,−2)

Decide whether or not the ordered pair satisfies the system of linear equations. -(3, -1); {x+y=−4x−y=−2\left\{ \begin{array} { l } x + y = - 4 \\x - y = - 2\end{array} \right.{x+y=−4x−y=−2​

Solve the system of equations by the addition method. - {3x−5y=−73x−5y=8\left\{ \begin{array} { l } 3 x - 5 y = - 7 \\3 x - 5 y = 8\end{array} \right.{3x−5y=−73x−5y=8​

Solve the system of equations by graphing the equations on the same set of axes. - {x+y=1x−y=5\left\{ \begin{array} { l } x + y = 1 \\x - y = 5\end{array} \right.{x+y=1x−y=5​

Answer true or false. -If the two equations in a system of linear equations are added and the result is 8 = 0, the system has no solution.

Answer true or false. -Although (7, 3)is not a solution of x + 3y = 2, it can still be a solution of the system {x+3y=2x+y=4\left\{ \begin{array} { l } x + 3 y = 2 \\x + y = 4\end{array} \right.{x+3y=2x+y=4​

Solve the system of equations by the addition method. - {3x−5y=32x−3y=3\left\{ \begin{array} { l } 3 x - 5 y = 3 \\2 x - 3 y = 3\end{array} \right.{3x−5y=32x−3y=3​

Is the ordered pair a solution of the linear system? - {2x−4y=65x+y=1;(1,−1)\left\{ \begin{array} { l } 2 x - 4 y = 6 \\5 x + y = 1\end{array} ; ( 1 , - 1 ) \right.{2x−4y=65x+y=1​;(1,−1)

Solve the problem. -The three angles in a triangle always add up to 180°. If one angle in a triangle is 114° and the second is 5 times the third, what are the three angles?

Solve the system of equations by the addition method. - {x+8y=−392x+8y=−46\left\{ \begin{array} { r } x + 8 y = - 39 \\2 x + 8 y = - 46\end{array} \right.{x+8y=−392x+8y=−46​

Solve the problem. -Julie and Eric row their boat (at a constant speed) 35 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of the current.

Answer true or false. -If the two equations in a system of linear equations are added and the result is 7x = 0, the system has no solution.

Solve the system of equations by the addition method. - {x+y=33x−y=13\left\{ \begin{array} { l } x + y = 33 \\x - y = 13\end{array} \right.{x+y=33x−y=13​

Write a system of equations to describe the situation. Do not solve the system. -One number is 5 more than another number. If you add 9 to 2 times the first number, the result is 3 times the second number.

Decide whether or not the ordered pair satisfies the system of linear equations. -(-6, 5); $\left\{ \begin{array} { l } x + y = - 1 \\x - y = - 11\end{array} \right.$

Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? - $\left\{ \begin{aligned}3 x - y & = 1 \\x + 4 y & = 22\end{aligned} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r r } 7 x + 2 y = & 9 \\- 2 x - 2 y = & - 24\end{array} \right.$

Solve the system by the substitution or the addition method. - $\left\{ \begin{array} { l } x + \frac { 1 } { 51 } y = 3 \\- 3 x + 2 y = 12\end{array} \right.$

Decide whether or not the ordered pair satisfies the system of linear equations. -(2, -6); $\left\{ \begin{array} { l } 4 x + y = 2 \\2 x + 4 y = - 20\end{array} \right.$

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 5 x - 3 y = 21 \\4 x + 5 y = - 3\end{array} ; \quad ( 3 , - 2 ) \right.$

Decide whether or not the ordered pair satisfies the system of linear equations. -(3, -1); $\left\{ \begin{array} { l } x + y = - 4 \\x - y = - 2\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 3 x - 5 y = - 7 \\3 x - 5 y = 8\end{array} \right.$

Answer true or false. -Although (7, 3)is not a solution of x + 3y = 2, it can still be a solution of the system $\left\{ \begin{array} { l } x + 3 y = 2 \\x + y = 4\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 3 x - 5 y = 3 \\2 x - 3 y = 3\end{array} \right.$

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 2 x - 4 y = 6 \\5 x + y = 1\end{array} ; ( 1 , - 1 ) \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r } x + 8 y = - 39 \\2 x + 8 y = - 46\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 33 \\x - y = 13\end{array} \right.$