How do you solve the system of equations #x+ 9y = - 10# and #2x + 6y = 4#?

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Answer 1 · 2017-03-04T13:25:22

See the entire solution process below:

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

#x + 9y = -10#

#x + 9y - color(red0(9y) = -10 - color(red)(9y)#

#x + 0 = -10 - 9y#

#x = -10 - 9y#

Step 2) Substitute #-10 - 9y# for #x# in the second equation and solve for #y#:

#2x + 6y = 4# becomes:

#2(-10 - 9y) + 6y = 4#

#(2 xx -10) + (2 xx -9y) + 6y = 4#

#-20 - 18y + 6y = 4#

#-20 - 12y = 4#

#color(red)(20) - 20 - 12y = color(red)(20) + 4#

#0 - 12y = 24#

#-12y = 24#

#(-12y)/color(red)(-12) = 24/color(red)(-12)#

#(color(red)(cancel(color(black)(-12)))y)/cancel(color(red)(-12)) = -2#

#y = -2#

Step 3) Substitute #-2# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = -10 - 9y# becomes:

#x = -10 - (9 xx -2)#

#x = -10 + 18#

#x = 8#

The solution is: #x = 8# and #y = -2# or #(8, -2)#