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

Answers

  1. Answer:
    x = 3
    (3, 13)
    Step-by-step 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)

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