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let's denote the first number with x, and the second number with y. So,

8x + 5y = -13

x + y = 1

y = 1 - x substitute 1 - x for y at the first equation;

8x + 5(1 - x) = -13

8x + 5 - 5x = -13

3x + 5 = -13 subtract 5 to both sides;

3x = -18 divide by 3 to both sides;

x = -6

y = 1 - x substitute -6 for x ;

y = 1 -(-6)

y = 1 + 6 = 7

Thus the numbers are -6 and 7.

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