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)

Step-by-step explanation:

We observe that the y-terms have coefficients 7 and -14. If we want to eliminate the y-terms, we need to multiply 7 by a factor that makes it be the opposite of -14. That factor will be -(-14)/7 = 2.

After multiplying the first equation by 2, we have ...

• 16x +14y = 78
• 4x -14y = -68

Adding these two equations gives ...

  20x = 10

Solving for x, we need to divide by 20:

  x = 10/20 = 1/2

Substituting this into the first equation, we get ...

  8(1/2) +7y = 39

  7y = 35 . . . . . . subtract 4

  y = 35/7 = 5 . . . divide by 7

Then the solution is (x, y) = (1/2, 5).

_____

Check

We used the first equation to find y, so we know the x- and y-values satisfy the first equation. We need to check the result using the second equation.

  4(1/2) -14(5) = -68

  2 -70 = -68 . . . . . . . true; result checks OK