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

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Question 1074770: Eight times a number plus five times another number is -13. The sum of the two numbers is 1. What are the numbers
Answer by Theo(13342) (Show Source):
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let x = one of the numbers
let y = the other number.

8x + 5y = -13

x + y = 1

solve for y in the second equation to get y = 1 - x

replace y with 1 - x in the first equation to getr 8x + 5 * (1 - x) = -13

simplify to get 8x + 5 - 5x = -13

combine like terms to get 3x + 5 = - 13

subtract 5 from both sides of the equation to get 3x = -18

solve for x to get x = -6

x + y = 1 becomes -6 + y = 1

solve for y to get y = 7

your solution should be x = -6 and y = 7

in the first equation, replace x with -6 and y with 7 to get 8x + 5y = -13 becomes 8 * -6 + 5 * 7 = -13

simplify this to get -48 + 35 = -13

combine like terms to get -13 = -13.

this confirms the solution is correct because both equations are true when x = -6 and y = 7.