How do you solve the following system?: $x + 2y = -2 , y=2x+9$

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How do you solve the following system?: $x + 2y = -2 , y=2x+9$

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Answer 1 · 2018-03-18T04:05:22

Substitution Property

$x=-4 and y =1$

Explanation:

If $x =$ a value, then $x$ will equal that same value no matter where it is or what it's being multiplied by.

Allow me to explain.

$x + 2y = -2$

$y = 2x + 9$

Replacing $y=2x+9$

$x + 2(2x + 9) = -2$

Distribute:

$x + 4x + 18 = -2$

Simplify:

$5x = -20$

$x = -4$

Since we know what $x$ is equal to, we can now solve for the $y$ value using this same philosophy.

$x = -4$

$x + 2y = -2$

$(-4) + 2y = -2$

Simplify

$2y = 2$

$y = 1$

$x = -4, y = 1$

Also, just as a general rule of thumb, if you're unsure of your answers in any system of equations like this, you can check your answers by plugging both x and y into both equations and seeing if a valid input is spit out. Like so:

$x + 2y = -2$

$y = 2x + 9$

$(-4) + 2(1) = -2$

Since $-2 is -2$ . We've solved the system of equations correctly.

$y = 2x + 9$

$1 = 2(-4) + 9$

$1 = -8 + 9$

$1 = 1.$

Hence it is verified that $x=-4 and y =1$

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How do you solve the following system?: $x + 2y = -2 , y=2x+9$

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Explanation:

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Math

Humanities

... and beyond

How do you solve the following system?: x + 2y = -2 , y=2x+9 x + 2y = -2 , y=2x+9

1 Answer

Explanation:

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How do you solve the following system?: $x + 2y = -2 , y=2x+9$