Twice a number minus a second number is -1. Twice the second number added to three times the first number is 9. How do you find the two numbers?

1 Answer
Dec 6, 2016

The first number is #1# and the second number is #3#.

Explanation:

We consider the first number as #x# and the second as #y#. From the data, we can write two equations:

#2x-y=-1#
#3x+2y=9#

From the first equation, we derive a value for #y#.

#2x-y=-1#

Add #y# to both sides.

#2x=-1+y#

Add #1# to both sides.

#2x+1=y# or #y=2x+1#

In the second equation, substitute #y# with #color(red)((2x+1))#.

#3x+2color(red)((2x+1))=9#

Open the brackets and simplify.

#3x+4x+2=9#

#7x+2=9#

Subtract #2# from both sides.

#7x=7#

Divide both sides by #7#.

#x=1#

In the first equation, substitute #x# with #color(red)1#.

#(2xxcolor(red)1)-y=-1#

#2-y=-1#

Add #y# to both sides.

#2=y-1#

Add #1# to both sides.

#3=y# or #y=3#