How do solve the following linear system?: # x+2y =2 , 5x - 3y = -29 #?

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Answer 1 · 2017-02-20T15:26:43

See the entire solution process below:

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

#x + 2y = 2#

#x + 2y - color(red)(2y) = 2 - color(red)(2y)#

#x + 0 = 2 - 2y#

#x = 2 - 2y#

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

#5x - 3y = -29# becomes:

#5(2 - 2y) - 3y = -29#

#10 - 10y - 3y = -29#

#10 - 13y = -29#

#-color(red)(10) + 10 - 13y = -color(red)(10) - 29#

#0 - 13y = -39#

#-13y = -39#

#(-13y)/color(red)(-13) = -39/color(red)(-13)#

#(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = 3#

#y = 3#

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

#x = 2 - 2y# becomes:

#x = 2 - (2 xx 3)#

#x = 2 - 6#

#x = -4#

The solution is: #x = -4# and #y = 3# or #(-4, 3)#