Question

1. how many solutions does the system have and what does it look like graphically? $-6x + 3y = -9$ and $-4x + 2y = -6$

a. no solution
b. one solution
c. infinite solutions
d. parallel lines
e. intersecting lines
f. single line

Explanation:

Step1: Simplify first equation

Simplify \(-6x + 3y = -9\) by dividing by 3:
\(\frac{-6x}{3} + \frac{3y}{3} = \frac{-9}{3}\)
\(-2x + y = -3\)
Rearrange: \(y = 2x - 3\)

Step2: Simplify second equation

Simplify \(-4x + 2y = -6\) by dividing by 2:
\(\frac{-4x}{2} + \frac{2y}{2} = \frac{-6}{2}\)
\(-2x + y = -3\)
Rearrange: \(y = 2x - 3\)

Step3: Analyze solutions and graph

Both equations simplify to the same line (\(y = 2x - 3\)). So, they have infinite solutions (all points on the line) and graph as a single line.

Answer:

C. Infinite Solutions
F. Single Line