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

The two numbers are -6 and 7

Solution:

Given that eight times a number plus five times another number is -13

The sum of two numbers is 1

To find: the two numbers

Let the two numbers be "a" and "b"

From given information,

Eight times a number plus five times another number = -13

eight times a number "a" + five times another number "b" = -13

8a + 5b = -13 eqn 1

Also given that sum of two numbers is 1

sum of two numbers = 1

a + b = 1 eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "b"

From eqn 2,

a = 1 - b eqn 3

Substitute eqn 3 in eqn 1

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

8 - 8b + 5b = -13

8 - 3b = -13

-3b = -13 - 8

-3b = -21

Substitute b = 7 in eqn 3

a = 1 - 7

Thus the two numbers are -6 and 7

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