Question

One number is greater than another by fifteen, if 5 times the larger number minus twice the smaller one is three? find the two numbers.

Answer 1

(-9,-24)

Explanation:

First set up a system of equations:

Set the bigger number to x and the smaller number to y

Here are the two equations:

`x=y+15` Note that you add 15 to y because it is 15 smaller than x.

and

`5x-2y=3`

From here there are a few ways to solve this system. The fastest way however would be to multiply the entire first equation by -2 to get:

`-2x=-2y-30`

rearranging this gives

`-2x+2y=-30`

Your two equations are

`-2x+2y=-30` and
`5x-2y=3`

You can now simply add the two functions together and cancel out the y term. This gives a single variable equation that you can solve:

`3x=-27`
Solving this gives x=-9

With your x value, you can now plug it in to either equation (whichever one you find easiest to work with) and solve for y.

`(-9)=y+15` Insert x=-9
`-9=y+15` Subtract 15 from both sides
`-24=y`

Now you have both your x and y values that satisfy the equation. You write them in the coordinate pair (-9,-24)

To check your answer, go back and plug in both numbers to the other equation.

`5(-9)-2(-24)=3`
`-45+48=3`
`3=3`