Question

A pair of equations is shown below: y = 7x − 8 y = 5x − 2 Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points) I need help with part b.

Answer 1

Part A

y = 5x - 2 .... start with the second equation

7x - 8 = 5x - 2 ... replace y with 7x-8, which is from the first equation

7x-8+8 = 5x-2+8 .... add 8 to both sides

7x = 5x+6

7x-5x = 5x+6-5x ... subtract 5x from both sides

2x = 6

2x/2 = 6/2 ..... divide both sides by 2

x = 3

Use x = 3 to find the value of y

y = 7x - 8

y = 7*3 - 8

y = 21 - 8

y = 13

We can use the other equation as well to get the same result for y

y = 5x - 2

y = 5*3 - 2

y = 15 - 2

y = 13

The solution is (x,y) = (3, 13)

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Part B

The lines intersect at (3,13)

This is If you graphed both equations on the same xy coordinate grid.

This point is on both lines at the same time; therefore, the coordinate values of this point satisfy both equations at the same time. As shown below

y = 7x - 8

13 = 7*3 - 8 .... plug in (x,y) = (3,13)

13 = 13 .... true equation; this point is on the first line

repeat for the second equation

y = 5x - 2

13 = 5*3 - 2

13 = 13 ... true equation; this point is on the second line

both equations are true when (x,y) = (3,13), so this point is on both lines at the same time.