Question

Part 1: Explain, in complete sentences, how you would use the graphing method to solve the following system of equations. (3 points) Part 2: Provide the solution to the system. (2 points) Part 3: Explain what the solution represents on the graph. (1 point)

3x – 6y = 12
9x + 2y = –24

Answer 1

Since both equations are of the form y=mx+b, they are both straight lines.

You need two points to draw a straight line.

1. So select a value for x and solve for y. That will give you one point to plot on the coordinate plane.

2. Select another value for x and solve for y. That gives you another point to plot on the coordinate plane.

3. Draw a straight line through both points.

Repeat steps 1 through 3 for the other equation.

Part 2;

Rearrange equation one;

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

Substitute into the second equation.

9(4+2y)+2y=-24 So y= -3

Plug y=-3 into the first equation

x=4+2(-3) so x=-2

(-2,-3) is the solution

Part 3:

The point (-2,-3) is the point of intersection between the two lines.

Answer 2

I suggest you download a free copy of geogebra so you see what it looks like when you graph the two equations.