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How do solve the following linear system?: $4 x + y = 6, x - 4 y = - 24$ $4x+y=6 , x-4y=-24$ ?

1 Answer

Dec 11, 2015

$(x, y) = (0, 6)$ $(x,y)=(0,6)$

Explanation:

Given:
[1] $XXX 4 x + y = 6$ $color(white)("XXX")4x+y=6$
[2] $XXX x - 4 y = - 24$ $color(white)("XXX")x-4y=-24$

Re-write [1] as
[3] $XXX y = 6 - 4 x$ $color(white)("XXX")y=6-4x$

Substitute $(6 - 4 x)$ $(6-4x)$ for $y$ $y$ in [2]
[4] $XXX x - 4 (6 - 4 x) = - 24$ $color(white)("XXX")x-4(6-4x)=-24$

Simplify [4]
[5] $color(white)("XXX")xcancel(-24)+4x=cancel(-24)$

[6] $color(white)("XXX")5x=0$

[7] $color(white)("XXX")x=0$

Substitute $0$ for $x$ in [1]
[8] $color(white)("XXX")4(0)+y=6$

[9] $color(white)("XXX")y=6$

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