Question

Need Help ASAP

y = 2x − 5
y = -6x + 3
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: Check your work. Verify your solution and show your work.

Part C: If the two equations are graphed, what does your solution mean?

Answer 1

Part A

Solve by substitution.

Given equations:

• y = 2x − 5
• y = -6x + 3

⇒ 2x - 5 = -6x + 3

⇒ 2x - 5 + 5 = -6x + 3 + 5

⇒ 2x = -6x + 8

⇒ 2x + 6x = -6x + 8 + 6x

⇒ 8x = 8

⇒ 8x ÷ 8 = 8 ÷ 8

⇒ x = 1

To find y, substitute the found value of x into one of the equations:

⇒ y = 2(1) - 5

⇒ y = 2 - 5

⇒ y = -3

Therefore, the solution is (1, -3)

Part B

Substituting x = 1 into the equations:

y = 2x − 5

⇒ y = 2(1) − 5

⇒ y = 2 − 5

⇒ y = -3

y = -6x + 3

⇒ y = -6(1) + 3

⇒ y = -6 + 3

⇒ y = -3

When x = 1, both equations return a y-value of -3. Therefore, the solution is verified.

Part C

If the two equations are graphed, the solution will be the point of intersection.