A first number plus twice a second number is 8. Twice the first number plus the second totals 34. Find the numbers.

Answer 1

Let the first number = A

Let the second number = B

First, write out the equations :

A + 2*B = 8

2*A + B = 34

Second, use the 1st equation to solve for either A or B. I'll choose 'A'

A + 2*B = 8

A = 8 - 2*B

Third, plug the value of 'A' into the 2nd equation & solve

2*A + B = 34

2*(8 - 2*B) + B = 34

16 - 4*B + B = 34

16 - 3*B = 34

-3*B = 18

B = -6

Forth, Plug that value of 'B' into either the 1st or 2nd equation and solve

A + 2*B = 8

A + 2*(-6) = 8

A - 12 = 8

A = 20

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Always check your work :

A + 2*B = 8

20 + 2*(-6) = 8

20 - 12 = 8

8 = 8

2*A + B = 34

2*20 + (-6) = 34

40 - 6 = 34

34 = 34

Correct!