How do you solve 3y=11-2x and 3x=y-11?

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Answer 1 · 2018-03-14T19:34:18

Doing some linear algebra, you find that x=-2 and y=5

Set up both equations so y (and coefficients) is alone on the left-hand side (LHS). The first one is already done for you:

$3 y = 11 - 2 x$ $3y=11-2x$
$y = 11 + 3 x$ $y=11+3x$

Multiply the second equation by 3, and then subtract equation 2 from equation 1:

$(y = 11 + 3 x) \cdot 3 \Rightarrow 3 y = 33 + 9 x$ $(y=11+3x)*3 rArr 3y=33+9x$

$3 y = 11 - 2 x$ $3y=11-2x$
$-$ $-$
$ul(3y=33+9x)$
$0=-22-11x$

Solving for x:

$11x=-22 rArr color(red)(x=-2)$

Now, pick either starting equation and plug in x to solve for y:

$y=11+3x rArr y=11+3(-2)$
$y=11-6 rArr color(blue)(y=5)$