Question

Eight times a number plus five another number is -13. The sum of the two numbers is 1. What are the numbers?

Answer 1

Eight *(a number) plus 5*(another number) is -13.

translates to:

8(x) + 5(y) = -13

The sum of (the number) and (the other number) is 1.

translates to:

(x) + (y) = 1


We have a system of two equations involving two unknowns: x and y.

$\rm 8x+5y=-13\\ ~~x+~~y=~~~~1$

We can easily solve the system using Substitution or Elimination. Let's use Elimination this time.

We'll multiply the second equation by -8 so that the x's match up.

$\rm ~~~8x+5y=-13\\ -8x-8y=-8$

When we add the equations together, the x's will fall out of the equation, summing to zero. The 5y and -8y will sum to -3y and the right hand side will sum to -21.

$\rm -3y=-21$

Divide by -3,

$\rm y=7$

Plug back into one of your original equations to find the value of x,

$\rm x+y=1\\ x+7=1$

Subtract 7,

$\rm x=-6$