How do you solve the system of equations #2x-y=7# and #-x+y=-4#?

1 Answer
Mar 15, 2018

See a solution process below:

Explanation:

Step 1) Solve the second equation for #y#:

#-x + y = -4#

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

#0 + y = -4 + x#

#y = -4 + x#

Step 2) Substitute #(-4 + x)# for #y# in the first equation and solve for #x#:

#2x - y = 7# becomes:

#2x - (-4 + x) = 7#

#2x + 4 - x = 7#

#2x - x + 4 = 7#

#2x - 1x + 4 = 7#

#(2 - 1)x + 4 = 7#

#1x + 4 = 7#

#x + 4 = 7#

#x + 4 - color(red)(4) = 7 - color(red)(4)#

#x + 0 = 3#

#x = 3#

Step 3) Substitute #3# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:

#y = -4 + x# becomes:

#y = -4 + 3x#

#y = -1#

The Solution Is:

#x = 3# and #y = -1#

Or

#(3, -1)#