How do you solve the following linear system: #4x + 5y = -3 , -x + y = 3#?

Replaced a #+# with #=# for the first equation; hopefully, this is what was intended.

2 Answers
Nov 13, 2015

Answer:

#x=-2#, #y=-1#.

Explanation:

From the second equation, we know that #y=3+x#.

So, the first equation becomes

#4x+5color(green)(y)=-3 -> 4x+5color(green)((3+x))=-3#

Expand the left memeber: #4x+15+5x = 9x+15#

So, #9x+15=-3 \iff 9x = -18 iff x=-2#

Knowing this, we obtain #y#, since #y=3+x=3-2=1#

Nov 13, 2015

Answer:

#(x,y)=(-2,1)#

Explanation:

Given
[1]#color(white)("XXX")4x+5y=-3#
[2]#color(white)("XXX")-x+y=3#

Multiply [2] by #4#
[3]#color(white)("XXX")-4x+4y=12#

Add [1] and [3]
[4]#color(white)("XXX")9y=9#

Divide [4] by #9#
[5]#color(white)("XXX")y=1#

Substitute #1# for #y# in [2]
[6]#color(white)("XXX")-x+(1)=3#

Subtract #1# from both sides of [6]
[7]#color(white)("XXX")-x=2#

Multiply both sides of [7] by #(-1)#
[8]#color(white)("XXX")x=-2#