Question

The sum of four times a number and five times another number is -28. The sum of nine times the first number and two times the second number is 11. What is the second number?

Answer 1

-8

Explanation:

If we let x and y represent the first and second numbers, respectively, we can write the problem statement as the equations ...

• 4x +5y = -28
• 9x +2y = 11

We can multiply the first equation by -9 and add 4 times the second equation to get an equation in y alone:

-9(4x +5y) +4(9x +2y) = -9(-28) +4(11)

-37y = 296 . . . . . simplify

296/-37 = y = -8 . . . . . divide by the coefficient of y

The second number is -8.