Question

A pair of equations is shown below:

y = 7x − 9
y = 3x − 1

Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)

Part B: What is the solution to the pair of equations? (4 points)

Answer 1

Part A: If you graph the pair of equations shown above both lines will intersect at one point and that is how you would solve the system of equations graphically. The y intercept and slope for each equation would be for y = 7x − 9 it would have a slope of 7 and y intercept of -9 and y = 3x − 1 would have a slope of 3 and y intercept of -1.

Part B:The solution to the pair of equations is (2,5)

Answer 2

If you graph y=7x-9 and y=3x-1 the two lines will intersect at one point. That is how you graphically "solve" the system of equations.

Both of these lines are of the form y=mx+b where m is the slope and b is the y-intercept.

So for y=7x-9, the slope is 7 and the y-intercept is -9

For y=3x-1, the slope is 3 and the y-intercept is -1

....

The solution for this system occurs when both coordinates are equal to each other so we can say:

7x-9=3x-1 subtract 3x from both sides

4x-9=-1 add 9 to both sides

4x=8 divide both sides by 4

x=2, making y=3x-1 become:

y=3(2)-1=6-1=5, so the solution to the system of equations is:

(2,5)