Question

Solve each system by graphing: 4x + 6y = -12 2x + 3y = 6

Answer 1

Answer: For the system given, there is no solution.

The slopes are the same for both equations, so the lines are parallel. With no intersection, there is no solution.

It may be easier to graph the system if you change the equations to slope intercept form  y = mx + b

That locates the y-intercept, b and you can use the slope, m to plot additional points to draw the lines.

The attachment shows the graph of this system of equations.

Step-by-step explanation:  Isolate y on the left

First equation:

4x + 6y = -12 Subtract 4x from both sides

6y = -4x -12   Divide both sides by 6

y = -4x/6 -12/6   Simplify

y = -2x/3 - 2   The y-intercept is -2, the slope is -2/3

Second equation:

2x + 3y = 6  Subtract 2x from both sides

3y = –2x + 6 . Divide both sides by 3

y = –2x/3 + 6/3  Simplify

y = –2x/3 +2   The y-intercept is -2, the slope is -2/3  

At this point we see that the slopes are the same, so the lines are parallel.

Answer 2

4x + 6y = -12
2x + 3y = 6