How do solve the following linear system?: # x+2y =2 , x - 3y = -6 #?

2 Answers
Noah G
Dec 28, 2015

Using substitution I have found the answer below.

Explanation:

x + 2y = 2
x = 2 - 2y
2 - 2y - 3y = -6
2 - 5y = -6
-5y = -8
y = #8/5#

x + 2(#8/5#) = 2
x + #16/5# = 2
x = #-6/5#

The solution set is (#-6/5#, #8/5#)

Júlio B.
Dec 28, 2015

#x = -1.2 " and " y = 1.6#

Explanation:

First, we need to isolate one variable - #x# in this case:
# x +2y = 2# becomes # x = 2 - 2y #.
Then, we take this "new value" of x and put in the second equation:
#(2 - 2y) -3y = -6# which becomes # y = 8/5 " or " 1.6# when solved.
Having this new value of #y#, we go back to the first equation and solve it, finding #x# :
#x = 2 - 16/5 = 10/5 - 16/5 = -6/5 " or" - 1.2#

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