Question

Follow the directions to solve the system of equations by elimination. 8x + 7y = 39 4x – 14y = –68 Multiply the first equation to enable the elimination of the y-term. Add the equations to eliminate the y-terms. Solve the new equation for the x-value. Substitute the x-value back into either original equation to find the y-value. Check the solution. The solution to the system of equations is

Answer 1

The solution is ( 1/2 , 5)

Explanation:

∵ 8x + 7y = 39 ⇒ (1)

∵ 4x - 14y = -68 ⇒ (2)

Multiply (1) by 2

16x + 14y = 78 ⇒ (3)

Add (2) and (3)

∴ 20x = 10 ⇒ x = 10 ÷ 20 = 1/2

∴ x = 1/2

By substitute in (1)

8(1/2) + 7y = 39 ⇒ 7y = 39 - 4 = 35 ⇒ y = 35 ÷ 7 = 5

∴ y = 5

∴ The solution is ( 1/2 , 5)

To check:

8(1/2) + 7(5) = 4 + 35 = 39 = R.H.S

4(1/2) - 14(5) = 2 - 70 = -68 = R.H.S