Question

Solve the following system of equations by graphing.

–4x + 3y = –12
–2x + 3y = –18


Graph b


Graph c


Graph a


Graph d
25 POINTS IF YOU ANSWER CORRECTLY

Answer 1

Graph b

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=(4)/(3)x-4\\\\for\ x=0\to y=(4)/(3)(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=3\to y=(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=(2)/(3)x-6\\\\for\ x=0\to y=(2)/(3)(0)-6=0-6=-6\to(0,\ -6)\\\\for\ x=3\to y=(2)/(3)(3)-6=2-6=-4\to(3,\ -4)`