How do solve the following linear system?: # 5x-5y=10 , -4x-14y=28 #?

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Answer 1 · 2017-02-09T14:18:43

See the entire solution process below:

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

#5x - 5y = 10#

#5x - 5y + color(red)(5y) = 10 + color(red)(5y)#

#5x - 0 = 10 + 5y#

#5x = 10 + 5y#

#(5x)/color(red)(5) = (10 + 5y)/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 10/color(red)(5) + (5y)/color(red)(5)#

#x = 2 + y#

Step 2) Substitute #2 + y# for #x# in the second equation and solve for #y#:

#-4x - 14y = 28# becomes:

#-4(2 + y) - 14y = 28#

#-8 - 4y - 14y = 28#

#color(red)(8) - 8 - (4 + 14)y = color(red)(8) + 28#

#0 - 18y= 36#

#-18y = 36#

#(-18y)/color(red)(-18) = 36/color(red)(-18)#

#(color(red)(cancel(color(black)(-18)))y)/cancel(color(red)(-18)) = -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 = 2 + y# becomes:

#x = 2 + (-2)#

#x = 0#

The solution is: #x = 0# and #y = -2#