Question

There are two mystery numbers. The sum of 6 times the first number and 2 times the second number is -8. The sum of 2 times the first number and 8 times the second number is 34. What are the two numbers?

Answer 1

We can find the value of these 2 numbers by setting up 2 equations

x = first number

y = second number

by the what the first sentence in the problem says, we can say that:

6x + 2y = -8

by what the second sentence in the problem says, we can say that:

2x + 8y = 34

now that we have our 2 equations, we can use elimination to get rid of one of the variables. I am going to multiply the second equation by -3, so that we can add the 2 equations together and x will be eliminated.

-3(2x + 8y = 34)

-6x - 24y = -102

now we can add the 2 equations together and solve for y

6x + 2y = -8

-6x -24y = -102

-22y = -110

y= 5

now that we have the value for y, we can plug in 5 for y in either equation and solve for x,

6x + 2y = -8

6x + 2(5) = -8

6x + 10 = -8

6x = -18

x = -3

the two numbers are 5 and -3

hope this helped