How do you solve the system of equations #-6x - 2y = 10# and #2x + 2y = 8#?

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Answer 1 · 2018-01-23T12:17:21

See a solution process below:

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

#2x + 2y = 8#

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

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

#x + y = 4#

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

#x + 0 = 4 - y#

#x = 4 - y#

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

#-6x - 2y = 10# becomes:

#-6(4 - y) - 2y = 10#

#(-6 xx 4) + (-6 xx -y) - 2y = 10#

#-24 + 6y - 2y = 10#

#-24 + (6 - 2)y = 10#

#-24 + 4y = 10#

#-24 + color(red)(24) + 4y = 10 + color(red)(24)#

#0 + 4y = 34#

#4y = 34#

#(4y)/color(red)(4) = 34/color(red)(4)#

#y = 17/2#

Step 2) Substitute #17/2# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#

#x = 4 - y# becomes:

#x = 4 - 17/2#

#x = (2/2 xx 4) - 17/2#

#x = 8/2 - 17/2#

#x = -9/2#

The Solution Is:

#x = -9/2# and #y = 17/2#

Or

#(-9/2, 17/2)#