How do solve the following linear system?: # 3x-8y=6, 5x+2y=2 #?

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Answer 1 · 2018-04-18T23:36:17

See a solution process below

#3x - 8y = 6 - - - eqn1#

#5x + 2y = 2 - - - eqn2#

Using elimination method..

#5 xx (3x - 8y = 6)#

#3 xx (5x + 2y = 2)#

#15x - 40y = 30 - - - eqn3#

#15x - 6y = 6 - - - eqn4#

Subtract #eqn3 and eqn4#

#-34y = 24#

#y = - 24/34#

#y = - 12/17#

Substitute the value of #y# into #eqn1#

#3x - 8y = 6#

#3x - 8(-12/17) = 6#

#3x + 96/17 = 6#

Multiply through by #17#

#17(3x) + 17(96/17) = 17(6)#

#51x + 96 = 102#

#51x = 102 - 96#

#51x = 6#

#x = 6/51#

#x = 2/17#

Hence;

#x = 2/17 and y = -12/17#