How do you solve $y=x-4$ and $y=-x+2$ ?

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Answer 1 · 2017-02-11T02:16:47

See the entire solution process below:

Step 1) Because the first equation is already solved for $y$ , substitute $x - 4$ for $y$ in the second equation and solve for $x$ :

$y = -x + 2$ becomes:

$x - 4 = -x + 2$

$x - 4 + color(red)(4) + color(blue)(x) = -x + 2 + color(red)(4) + color(blue)(x)$

$x + color(blue)(x) - 4 + color(red)(4) = -x + color(blue)(x) + 2 + color(red)(4)$

$1x + color(blue)(1x) - 0 = 0 + 6$

$2x = 6$

$(2x)/color(red)(2) = 6/color(red)(2)$

$(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 3$

$x = 3$

Step 2) Substitute $3$ for $x$ in the first equation and calculate $y$ :

$y = x - 4$ becomes:

$y = 3 - 4$

$y = -1$

The solution is: $x = 3$ and $y = -1$ or $(3, -1)$

How do you solve y=x-4y=x-4 and y=-x+2y=-x+2?