How do you solve the system #5x - y = - 14 + 2x + y# and #7x + 9y + 4 = 3x + 8y#?

1 Answer
Feb 6, 2017

Answer:

#x=-2# and #y=4#

Explanation:

First simplify both equations:
#5x-y=-14+2x+y#

Subtract #2x# and #y# from both sides.

#3x-2y=-14#

#color(red)(7x+9y+4=3x+8y)#

Subtract #3x# and #8y# from both sides.

#color(red)(4x+y+4=0)#

Subtract #4# from each side.

#color(red)(4x+y=-4)#

So now we have two simplified equations:
#3x-2y=-14#
#color(red)(4x+y=-4)#

Using the second equation, determine a value for #y#.

#color(red)(4x+y=-4)#

Subtract #4x# from both sides.

#color(red)(y=-4-4x)#

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

#3x-2y=-14#

#3x-2color(red)((-4-4x))=-14#

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

#3x+color(red)(8+8x)=-14#

#11x+8=-14#

Subtract #8# from each side.

#11x=-22#

Divide both sides by #11#.

#x=-2#

In the second equation, substitute #x# with #color(blue)(-2)#.

#color(red)(4x+y=-4)#

#color(red)(4color(blue)((-2))+y=-4)#

Open the brackets and simplify. The product of a positive and a negative results in a negative.

#color(red)(-8+y=-4)#

Add #8# to both sides.

#color(red)(y=4)#