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

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.



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.



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.



Divide by -3,



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



Subtract 7,