How do you solve the system of equations #3x - 8y = - 47# and #x - 6y = - 59#?

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Answer 1 · 2017-05-10T22:47:28

See a solution process below: #(-577/17, 71/17)#

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

#x - 6y = -59#

#x - 6y + color(red)(6y) = -59 + color(red)(6y)#

#x - 0 = -59 + 6y#

#x = -59 + 6y#

Step 2) Substitute #-59 + 6y# for #x# into the first equation and solve for #y#:

#3x - 8y = -47# becomes:

#3(-59 + 6y) - 8y = -47#

#(3 * -59) + (3 * 6y) - 8y = -47#

#-177 + 18y - 8y = -47#

#-177 + 10y = -47#

#color(red)(177) - 177 - 17y = color(red)(177) - 47#

#0 + 10y = 130#

#10y = 130#

#(10y)/color(red)(10) = 130/color(red)(10)#

#(color(red)(cancel(color(black)(10)))y)/cancel(color(red)(10)) = 130/10#

#y = 13#

Step 3) Substitute #13# for #y# into the solution for the second equation at the end of Step 1 and calculate #x#:

#x - 6y = -59# becomes:

#x - (6 * 13) = -59#

#x - 78 = -59#

#x - 78 + color(red)(78) = -59 + color(red)(78)#

#x - 0 = 19#

#x = 19#

The solution is: #x = 19# and #y = 13# or #(19, 13)#