How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $y = -x - 4$ and $y = x + 2$ ?

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Answer 1 · 2017-05-29T14:57:08

See a solution process below:

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

$y = x + 2$ becomes:

$-x - 4 = x + 2$

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

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

$-6 = 2x$

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

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

$-3 = x$

$x = -3$

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

$y = -x - 4$ becomes:

$y = -(-3) - 4$

$y = 3 - 4$

$y = -1$

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

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent y = -x - 4y = -x - 4 and y = x + 2y = x + 2?