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,
\(\rm x=-6\)
