Question

ONE QUESTION ONLY!!!

Please show work!
49 points!

Marco is thinking of two numbers. Adding 5 times the first number and 8 times the second number gives a total of -13. Also, adding 5 times the first number and 10 times the second number gives -15. What are the two numbers?

Answer 1

1st number be x, 2nd number be y

Adding 5 times the first number and 8 times the second number gives a total of -13

so 5x+8y=-13

Adding 5 times the first number and 10 times the second number gives -15

so 5x+10y=-15

subtracting the above two eqns

(5x+8y)-(5x+10y) = -13-(-15)

-2y=2

y=-1

put back in first eqn 5x+8(-1)=-13

5x=-5

x=-1

Answer 2

Let first number = X and 2nd number = Y

Equation 1: 5X + 8Y = -13

Equation 2: 5X + 10Y = -15

Multiply equation 1 by -1 to get: -5X + -8Y = 13

Now add the 2 equations together:
-5X + 5X = 0

-8Y + 10Y = 2Y

13 + -15 = -2

The total of the 2 equations is 2Y = -2

divide both sides by 2 to solve for Y
Y = -2 / 2
Y = -1
Now we know the 2nd number is -1, so replace Y in the 1st equation and solve for X

5X +8(-1) = -13

5x + -8 = -13

Add 8 to both sides:
5x = -5

Divide both sides by 5 to get x

X = -5 / 5
X = -1

Both numbers are -1

To check replace X and Y with -1 and solve:

1st equation: 5(-1) +8(-1) = -5 + -8 = -13 TRUE

2nd equation: 5(-1) +10(-1) = -5 + -10 = -15 TRUE

Both numbers are -1