How do you solve x + y = 12 and y = 2x?

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Answer 1 · 2015-10-15T21:36:56

You can solve it like this:

We have 2 simultaneous equations:

$x + y = 12 (1)$ $x+y=12" "color(red)((1))$

$y = 2 x (2)$ $y=2x" "color(red)((2))$

From $(1)$ $color(red)((1))$ we can write:

$y = (12 - x)$ $y=(12-x)$

Substituting this value of $y$ $y$ into $(2)$ $color(red)((2))$ gives:

$(12 - x) = 2 x$ $(12-x)=2x$

$12 = 3 x$ $12=3x$

$x = \frac{12}{3} = 4$ $x=12/3=4$

Substituting this value of $x$ $x$ into $(1)$ $color(red)((1))$ gives:

$4 + y = 12$ $4+y=12$

$y = 12 - 4$ $y=12-4$

$y = 8$ $y=8$