How do you solve the following linear system -x + 2y = 6 , x - 4y = -3 ?

1 Answer
Dec 14, 2015

color(white)(xx)x=-9color(white)(x) "and" color(white)(x)y=-3/2

Explanation:

color(white)(xx)-x+2y=6, x-4y=-3

With a different approach:
color(white)(xx)-x+2y=6<=>color(red)(y=(x+6)/2)
and
color(white)(xx)x-4y=-3<=>color(red)(y=(x+3)/4)

color(white)(xx)(x+6)/2=y
=>(x+6)/2=color(blue)((x+3)/4)

Multiply both side by color(green)4 to simplify right side:
color(white)(xx)color(green)(4xx)(x+6)/2=color(green)(4xx)(x+3)/4
=>color(red)2x+color(red)12=x+3

Finally add color(red)(-x-12) to both side to find x.
=>2x+12color(red)(-x-12)=x+3color(red)(-x-12)
=>x=-9

color(white)(xx)y=(x+6)/2
color(white)(xxx)=(color(blue)(-9)+6)/2
color(white)(xxx)=-3/2