How do you solve this system of equations: #2x + 4y = - 8; 2x + 7y = - 20#?

1 Answer
Jan 30, 2018

See a solution process below:

Explanation:

Step 1) Solve the first equation for #x#:

#2x + 4y = -8#

#(2x + 4y)/color(red)(2) = -8/color(red)(2)#

#(2x)/color(red)(2) + (4y)/color(red)(2) = -4#

#x + 2y = -4#

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

#x + 0 = -4 - 2y#

#x = -4 - 2y#

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

#2x + 7y = -20# becomes:

#2(-4 - 2y) + 7y = -20#

#(2 xx -4) - (2 xx 2y) + 7y = -20#

#-8 - 4y + 7y = -20#

#-8 + (-4 + 7)y = -20#

#-8 + 3y = -20#

#-8 + color(red)(8) + 3y = -20 + color(red)(8)#

#0 + 3y = -12#

#3y = -12#

#(3y)/color(red)(3) = -12/color(red)(3)#

#y = -4#

Step 3) Substitute #-4# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = -4 - 2y# becomes:

#x = -4 - (2 xx -4)#

#x = -4 - (-8)#

#x = -4 + 8#

#x = 4#

The Solution Is:

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

Or

#(4, -4)#