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
Apr 19, 2018

(-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