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

Answer 1

Substitution Property

#x=-4 and y =1#

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

Let me clarify.

#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#

As a general rule of thumb, you can verify your answers in any system of equations similar to this one by entering both x and y into both equations and observing whether a valid input is returned. For example:

#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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Answer 2

To solve the system of equations (x + 2y = -2) and (y = 2x + 9), you can use substitution or elimination method. Here's how to do it using the substitution method:

  1. Substitute (y) in the first equation with the expression from the second equation: [ x + 2(2x + 9) = -2 ]

  2. Simplify the equation: [ x + 4x + 18 = -2 ] [ 5x + 18 = -2 ] [ 5x = -20 ] [ x = -4 ]

  3. Substitute the value of (x) back into the second equation to find (y): [ y = 2(-4) + 9 ] [ y = -8 + 9 ] [ y = 1 ]

So, the solution to the system of equations is (x = -4) and (y = 1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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