How do I find the solution to the problem -7x+y= -19 and -2x+3y= -19?

Question

I need to find a solution for this problem using the method of elimination.
Thanks!

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Answer 1 · 2016-11-18T15:40:01

#x = 2# and #y = -5#

Step 1) Solve the first equation for #y# while keeping the equation balanced:

#-7x + y + 7x = -19 + 7x#

#y = -19 + 7x#

Step 2) Substitute #-19 + 7x# for #y# in the second equation and solve for #x# while keeping the equation balanced:

#-2x + 3(-19 + 7x) = -19#

#-2x - 57 + 21x = -19#

#19x - 57 = - 19#

#19x - 57 + 57 = -19 + 57#

#19x = 38#

#(19x)/19 = 38/19#

#x = 2#

Step 3) Substitute #2# for #x# in the first equation and calculate #y#:

#y = -19 + (7*2)#

#y = -19 + 14#

#y = -5#