# Solving Linear Systems by Graphing Worksheet

Solving Linear Systems by Graphing Worksheet
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1.
How many solutions does the system of linear inequalities - $x$ + 2$y$ ≥ 6 and $x$ - 2$y$ ≥ 4 have?
 a. finite b. 1 c. infinite

2.
Which of the graphs represent the system of equations - 2$x$ + 3$y$ > 6 and $x$ + $y$ ≤ - 3?

 a. Graph 3 b. Graph 1 c. Graph 2 d. Graph 4

3.
Choose a graph that represents the following system of inequalities.
$x$ ≥ 0
$y$ ≥ 0
4$x$ + 6$y$ ≤ 12

 a. Graph 2 b. Graph 4 c. Graph 1 d. Graph 3

4.
Which of the following linear systems matches the graph?

 a. $y$ = $x$ + 2, $y$ = $\frac{1}{4}$$x$ - 3 b. $y$ = - $x$ - 2, $y$ = $\frac{1}{4}$$x$ + 3 c. $y$ = $x$ - 2, $y$ = $\frac{1}{4}$$x$ + 3 d. $y$ = - $x$ + 2, $y$ = $\frac{1}{4}$$x$ - 3

5.
Find the number of solutions for the linear system.
- 2$x$ + $y$ = - 4
- 10$x$ + 5$y$ = - 20
 a. exactly one solution b. exactly two solutions c. infinitely many solutions d. no solution

6.
Find the number of solutions for the linear system.
$x$ + $y$ = - 4
$x$ + $y$ = - 1
 a. exactly one solution b. no solution c. exactly two solutions d. infinitely many solutions

7.
How many solutions do the systems of linear inequalities - $x$ + 2$y$ ≥ 6 and $x$ - 2$y$ ≥ 4 have?
 a. infinite b. finite c. 1

8.
Which of the graphs represents the system of equations, - 2$x$ + 3$y$ > 6 and $x$ + $y$ ≤ - 3?

 a. Graph 4 b. Graph 1 c. Graph 3 d. Graph 2

9.
Choose a graph that represents the system of inequalities:
$x$ ≥ 0
$y$ ≥ 0
4$x$ + 6$y$ ≤ 12

 a. Graph 3 b. Graph 4 c. Graph 2 d. Graph 1

$x$ + 4$y$ = 1
$x$ + 4$y$ = - $\frac{1}{2}$