Question 1

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
x + y = - 12 \
x - y = - 12
\end{array} \right.$

Accepted Answer

A) (0, 12) 
B) (-12, 0) 
C) (12, 0) 
D) (0, -12) 
A) (0, 12) 
B) (-12, 0) 
C) (12, 0) 
D) (0, -12)

Question 2

Solve the problem by writing and using a system of linear equations.
-Two bikers start at opposite ends of a trail and bike toward each other. The trail is 132 miles long and they meet in 4 hours. If one biker is twice as fast as the other, find both biking speeds.

Accepted Answer

A) 9 mph, 18 mph 
B) 4 mph, 8 mph 
C) 11 mph, 22 mph 
D) 66 mph, 132 mph 
A) 9 mph, 18 mph 
B) 4 mph, 8 mph 
C) 11 mph, 22 mph 
D) 66 mph, 132 mph

Question 3

Solve the system of equations by graphing the equations on the same set of axes.
-$$\left\{ \begin{aligned}
x + \frac { 1 } { 3 } y & = 4 \
x & = 2
\end{aligned} \right.$$

Accepted Answer

A) (2, -6) 
B) (2, 6) 
C) (-2, 6) 
D) no solution 
A) (2, -6) 
B) (2, 6) 
C) (-2, 6) 
D) no solution

Question 4

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { r } 
x + y = - 10 \
y = - 3 x
\end{array} \right.$

Accepted Answer

A) (5, -15) 
B) (-15, 5) 
C) infinite number of solutions 
D) no solution 
A) (5, -15) 
B) (-15, 5) 
C) infinite number of solutions 
D) no solution

Question 5

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
\frac { 1 } { 2 } x + 3 y = - \frac { 23 } { 4 } \
4 x = - y
\end{array} \right.$

Accepted Answer

A)  $\left( \frac { 1 } { 4 } , - 1 \right)$ 
B) (2, 2) 
C) (0, 0) 
D)  $\left( \frac { 1 } { 2 } , - 2 \right)$ 
A)  $\left( \frac { 1 } { 4 } , - 1 \right)$ 
B) (2, 2) 
C) (0, 0) 
D)  $\left( \frac { 1 } { 2 } , - 2 \right)$

Question 6

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores.  
-In what years was the number of General stores greater than the number of Acme stores?

Accepted Answer

A) 2000 through 2002 
B) 1192 through 1998 
C) 1999 through 2002 
D) 1992 through 1999 
A) 2000 through 2002 
B) 1192 through 1998 
C) 1999 through 2002 
D) 1992 through 1999

Question 7

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
- 6 x - 24 y = 6 \
2 x + 8 y = 0
\end{array} \right.$

Accepted Answer

A) (0, 6) 
B) (6, 0) 
C) infinite number of solutions 
D) no solution 
A) (0, 6) 
B) (6, 0) 
C) infinite number of solutions 
D) no solution

Question 8

Solve the problem by writing and using a system of linear equations.
-Find the amount of a 11% saline solution a lab assistant should add to 60 cc (cubic centimeters)of a 21% in order to have 14% solution.

Accepted Answer

A) 40 cc 
B) 10 cc 
C) 190 cc 
D) 140 cc 
A) 40 cc 
B) 10 cc 
C) 190 cc 
D) 140 cc

Question 9

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?
-$\left\{ \begin{array} { l } 
x + y = 6 \
x + y = 3
\end{array} \right.$

Accepted Answer

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

Question 10

Solve the problem.
-Kelly is a partner in an Internet-based seed and garden supply business. The company offers a blend of exotic wildflower seeds for $105 per pound and a blend of common wildflower seeds for $15 per pound. Kelly is Creating a medium-price product by mixing together 32 pounds of the more expensive blend with 7 pounds of The less expensive blend. What will be the price per pound for the new blend? (Round to the nearest cent, if Necessary.)

Accepted Answer

A) $28.88 per pound 
B) $10.13 per pound 
C) $88.85 per pound 
D) $31.15 per pound 
A) $28.88 per pound 
B) $10.13 per pound 
C) $88.85 per pound 
D) $31.15 per pound

Question 11

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
y = 1.2 x - 2.3 \
y = 0.8 x - 2.02
\end{array} \right.$

Accepted Answer

A) (0.7, -1.46) 
B) (-0.7, -1.46) 
C) infinite number of solutions 
D) no solution 
A) (0.7, -1.46) 
B) (-0.7, -1.46) 
C) infinite number of solutions 
D) no solution

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = - 12 \\x - y = - 12\end{array} \right.$

Solve the problem by writing and using a system of linear equations. -Two bikers start at opposite ends of a trail and bike toward each other. The trail is 132 miles long and they meet in 4 hours. If one biker is twice as fast as the other, find both biking speeds.

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x + y = - 10 \\y = - 3 x\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + 3 y = - \frac { 23 } { 4 } \\4 x = - y\end{array} \right.$

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores. -In what years was the number of General stores greater than the number of Acme stores?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 6 x - 24 y = 6 \\2 x + 8 y = 0\end{array} \right.$

Solve the problem by writing and using a system of linear equations. -Find the amount of a 11% saline solution a lab assistant should add to 60 cc (cubic centimeters)of a 21% in order to have 14% solution.

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? - $\left\{ \begin{array} { l } x + y = 6 \\x + y = 3\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } y = 1.2 x - 2.3 \\y = 0.8 x - 2.02\end{array} \right.$

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Exam 11: Systems of Equations

Solve the system of equations by the addition method. - {x+y=−12x−y=−12\left\{ \begin{array} { l } x + y = - 12 \\x - y = - 12\end{array} \right.{x+y=−12x−y=−12​