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How do you solve the system $4 x - y = 9$ $4x-y=9$ and $x - 3 y = 16$ $x-3y=16$ ?

1 Answer

Jun 4, 2015

$(x, y) = (1, - 5)$ $(x,y)=(1,-5)$

Explanation:

Given
[1] $XXXX$ $color(white)("XXXX")$ $4 x - y = 9$ $4x-y = 9$
[2] $XXXX$ $color(white)("XXXX")$ $x - 3 y = 16$ $x-3y = 16$

Re-arrange the terms of [2] to get
[3] $XXXX$ $color(white)("XXXX")$ $x = 3 y + 16$ $x = 3y+16$

Using [3] substitute $(3 y + 16)$ $(3y+16)$ for $x$ $x$ in [1]
[4] $XXXX$ $color(white)("XXXX")$ $4 (3 y + 16) - y = 9$ $4(3y+16)-y = 9$

Simplifying
[5] $XXXX$ $color(white)("XXXX")$ $11 y + 64 = 9$ $11y +64 = 9$
[6] $XXXX$ $color(white)("XXXX")$ $11 y = - 55$ $11y = -55$
[7] $XXXX$ $color(white)("XXXX")$ $y = - 5$ $y = -5$

Using [7] substitute $(- 5)$ $(-5)$ for $y$ $y$ in [1]
[8] $XXXX$ $color(white)("XXXX")$ $4 x - (- 5) = 9$ $4x - (-5) = 9$
[9] $XXXX$ $color(white)("XXXX")$ $4 x = 4$ $4x = 4$
[10] $XXXX$ $color(white)("XXXX")$ $x = 1$ $x = 1$

$(x, y) = (1, - 5)$ $(x,y) = (1,-5)$

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