How do you solve the system of linear equations #5x - 4y = 7, 2y + 6x = 22#?

1 Answer
Dec 5, 2016

Answer:

#x=3# and #y=2#.

Explanation:

#5x-4y=7#
#2y+6x=22#

From the second equation, we can determine a value for #4y#.

#2y+6x=22#

Multiply all terms by #2#.

#4y+12x=44#

Subtract #12x# from both sides.

#4y=44-12x#

In the first equation, replace #4y# with #color(red)((44-12x))#.

#5x-4y=7#

#5x-color(red)((44-12x))=7#

Open the brackets and simplify. The product of two negatives i a positive.

#5x-color(red)(44+12x)=7#

#17x-44=7#

Add #44# to both sides.

#17x=51#

Divide both sides by #17#.

#x=3#

In the second equation, substitute #x# with #3#.

#2y+6x=22#

#2y+(6xx3)=22#

#2y+18=22#

Subtract #18# from both sides.

#2y=4#

Divide both sides by #2#.

#y=2#