# 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.

##### 1 Answer

(-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:

*smaller* than x.

and

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:

rearranging this gives

Your two equations are

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:

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.

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.