How do solve the following linear system?: # 4x-2y=2 , x-3y=-2 #?

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Answer 1 · 2016-10-07T17:36:51

#"solution : x=1 and y=1 "#

#"given :"#

#4x-2y=2" (1)"#

#x-3y=-2" (2)"#

#"expand both side of equation (2) by 4 "#

#4(x-3y)=-2*4#

#4x-12y=-8#

#color(red)(4x)=12y-8" (3)"#
#"rearrange (1)"#

#color(red)(4x)=2y+2" (4)"#

#"(3) and (4) are equal."#

#12y-8=2y+2#

#12y-2y=2+8#

#10y=10#

#y=1#

#"now use (1) or (2)"#

#4x-2*1=2#

#4x-2=2#

#4x=2+2#

#4x=4#

#x=1#