How do you solve the system of equations #-7x - 4y = 5# and #- 7x + y = - 10#?

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Answer 1 · 2017-04-09T21:35:24

See the entire solution process below:

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

#color(red)(7x) - 7x + y = color(red)(7x) - 10#

#0 + y = 7x - 10#

#y = 7x - 10#

Step 2) Substitute #7x - 10# for #y# in the first equation and solve for #x#:

#-7x - 4y = 5# becomes:

#-7x - 4(7x - 10) = 5#

#-7x - (4 xx 7x) + (4 xx 10) = 5#

#-7x - 28x + (4 xx 10) = 5#

#-35x + 40 = 5#

#-35x + 40 - color(red)(40) = 5 - color(red)(40)#

#-35x + 0 = -35#

#-35x = -35#

#(-35x)/color(red)(-35) = (-35)/color(red)(-35)#

#(color(red)(cancel(color(black)(-35)))x)/cancel(color(red)(-35)) = 1#

#x = 1#

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

#y = 7x - 10# becomes:

#y = (7 xx 1) - 10#

#y = 7 - 10#

#y = -3#

The solution is: #x = 1# and #y = -3# or #(1, -3)#