Question

Solve the following system of equations by graphing.

Answer 1

Answer:

Graph b

Step-by-step explanation:

The equation of a linear function in slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The graph of linear function is a straight line therefore we need only two points to the plotting the graph.

$-4x+3y=-12\qquad\text{add 4x to both sides}\\\\3y=4x-12\qquad\text{divide both sides by 3}\\\\y=\dfrac{4}{3}x-4\\\\for\ x=0\to y=\dfrac{4}{3}(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=3\to y=\dfrac{4}{3}(3)-4=4-4=0\to(3,\ 0)$

$-2x+3y=-18\qquad\text{add 2x to both sides}\\\\3y=2x-18\qquad\text{divide both sides by 3}\\\\y=\dfrac{2}{3}x-6\\\\for\ x=0\to y=\dfrac{2}{3}(0)-6=0-6=-6\to(0,\ -6)\\\\for\ x=3\to y=\dfrac{2}{3}(3)-6=2-6=-4\to(3,\ -4)$