How do solve the following linear system?: # x - 3y = 8 , 3y = 15 -6x #?

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Answer 1 · 2015-12-05T03:30:43

The solution for the system of equations is :

#color(blue)(x=23/7, y=(-11)/7#

#x-3y=8#

#x=color(blue)(8 +3y#....................equation #1#

#3y=15-6x#................equation #2#

Solving by substitution.

Substituting equation #1# in #2#

#3y=15-6x#

#3y=15-6 * (color(blue)(8 +3y))#

#3y=15- 48 -18y#

#3y+18y=15- 48#

#21y=- 33#

#y=(-cancel33)/cancel21#

#color(blue)(y=(-11)/7#

Now, we substitute this value of #y# in equation #1# to find #x#

#x=8 +3y#

#x=8 +3 * (-11/7)#

#x=8 -33 /7#

#x=56/7 -33 /7#

#color(blue)(x=23/7#