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.

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Answer 1 · 2018-04-19T22:03:29

(-9,-24)

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#