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

9514 1404 393

Answer:

(x, y) = (1/2, 5)

Explanation:

The first equation multiplied by 2 is ...

16x +14y = 78

Then adding the second equation gives ...

(16x +14y) +(4x -14y) = (78) +(-68)

20x = 10 . . . . . . . . . simplify to get the "new equation"

x = 10/20 = 1/2 . . . . divide by 20 to solve for x

8(1/2) +7y = 39 . . . . substitute for x in the first equation

7y = 35 . . . . . . . . . subtract 4

y = 5 . . . . . . . . . . .divide by 7

The solution to the system of equations is (x, y) = (1/2, 5).