Question 257029
Let x = "a number
Let y = "another number"
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Write an equation for each statement:
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"eight times a number plus five times another number is -13."
8x + 5y = -13
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"the sum of the two numbers is 1."
x + y = 1
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what are the numbers. 
We can us elimination here if you want.
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Multiply the above equation by 5 and subtract from the 1st equation
8x + 5y = -13
5x + 5y = 5
----------------Subtraction eliminates y find x
3x = -18
x = {{{(-18)/3}}}
x = -6
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Find x using x + y = 1
-6 + y = 1
y = 1 + 6
y = 7
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Solution x = -6, y = 7
:
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Check solution in the 1st statement
eight times a number plus five times another number is -13
8(-6) + 5(7) = 
-48 + 35 = -13; confirms our solutions