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

Multiply the first equation by 2: 16x + 14y = 78.

Add this to the second equation:
(16x + 14y) + (4x − 14y) = 78 + (−68)
20x = 10
x = 10/20 = 1/2.

Substitute x = 1/2 into 8x + 7y = 39:
8(1/2) + 7y = 39 → 4 + 7y = 39 → 7y = 35 → y = 5.

Check in the second equation: 4(1/2) − 14(5) = 2 − 70 = −68 ✔

The solution is (1/2, 5).