Question 2 (essay worth 10 points)

(08.02 mc)

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)

You can solve a system of equations by graphing them, they will intersect at the coordinates of (x,y) where the two equations are equal to one another.

The slope-intercept form of a line is:

y=mx+b, where m is the slope and b=y-intercept (value of y when x=0)

y=7x-9, slope=7, y-intercept is (0, -9)

y=3x-1, slope=3, y-intercept is (0, -1)

Part B

If a solution exists, the coordinates of each equation are the same, so we can say y=y, which means:

7x-9=3x-1  add 9 to both sides

7x=3x+8  subtract 3x from both sides

4x=8  divide both sides by 4

x=2, now you can use either original equation to solve for the corresponding value of y...

y=3x-1 becomes:

y=3(2)-1

y=6-1

y=5

So the solution to the system of equations is the point (2, 5)