How do you solve the system of equations #7x + 3y = - 14# and #- 7x + y = 42#?

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Answer 1 · 2016-11-28T14:47:05

#x = -5# and #y = 7#

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

#-7x + y = 42#

#-7x + y + 7x = 42 + 7x#

#y = 42 + 7x#

Step 2) Substitute #42 + 7x# for #y# in the first equation and solve for #x#:

7x + 3(42 + 7x) = -14#

#7x + 126 + 21x = -14#

#28x + 126 = -14#

#28x + 126 - 126 = -14 - 126#

#28x = -140#

#(28x)/28 = (-140)/28#

#x = -5#

Step 3) Substitute #5# for #x# in the solution from Step 1) to calculate #y#:

#y = 42 + 7*(-5)#

#y = 42 - 35#

#y = 7#