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Question: Find the number of solutions the linear system has by using the graphing method.
- 3x + 2y = - 5
- 12x + 8y = - 20


A ) Exactly one solution
B ) No solution
C ) Infinitely many solutions
D ) Two solutions

Steps to derive

1 - 3x + 2y = - 5
 [Equation 1.]

2 - 12x + 8y = - 20
 [Equation 2.]

3 y = 32x - 52
 [Rearrange equation 1 in slope-intercept form.]

4 y = 32x - 52
 [Rearrange equation 2 in slope-intercept form.]

5 Graph both the equations using the slope and the y-intercept.


6 Both the equations represent the same line. So, each point on the line is a solution of the system.

7 So, the linear system has infinitely many solutions.



Hence the right answer is Option C

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