How do you solve 4x - 3y = 33 and x = - 4y - 25?

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Answer 1 · 2016-04-25T16:09:31

Point of intersection (lines cross) $->(x,y)=(3,-7)$

Given:

$4x-3y=33$ .................................(1)
$x=-4y-25$ .................................(2)

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$color(blue)("Determine the common value of y")$

Using equation (2) substitute for $x$ in equation (1)

$4(-4y-25)-3y=33color(white)(.).........................(1_a)$

$-16y-100-3y=33$

$-19y-100=33$

Multiply both sides by (-1)

$+19y+100=-33$

Subtract 100 from both sides

$19y+0=-133$

Divide both sides by 19

$color(blue)(y=-133/19 = -7)$
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$color(blue)("Determine the common value of "x)$

Substitute the value of $y$ into equation (2)

$color(brown)(x=-4y-25)" "color(green)( ->" " x=-4(-7)-25)$

$color(blue)(x=+3)$
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