Question

50 POINTS

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.

Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer

Answer 1

(3, 13) where x is 3 and y is 13

Answer 2

x = 3

(3, 13)

Explanation:

Given equations:

• y = 7x − 8
• y = 5x − 2

Part A

Solve by substitution:

⇒ y = y

⇒ 7x - 8 = 5x - 2

Subtract 5x from both sides:

⇒ 7x - 8 - 5x = 5x - 2 - 5x

⇒ 2x - 8 = - 2

Add 8 to both sides:

⇒ 2x - 8 + 8 = - 2 + 8

⇒ 2x = 6

Divide both sides by 2:

⇒ 2x ÷ 2 = 6 ÷ 2

⇒ x = 3

Part B

To find the y-value of the point of intersection, substitute the found value of x (from part A) into one of the equations:

⇒ y = 7(3) - 8

⇒ y = 21 - 8

⇒ y = 13

Therefore, the point at which the lines intersect is (3, 13)