SOLUTION: solve by elimination. 4x-y=9 and x-3y=16

Question 258185: solve by elimination. 4x-y=9 and x-3y=16
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
solve by elimination. 4x-y=9 and x-3y=16

Let's look at these equations laid out like this:
4x-y=9
x-3y=16(What if we multiplied this whole equation by -4). Let's do that below:

4x - y = 9
-4x + 12y = -64 See how we multiplied everything by 4? NOW what would happen if we added these two equations?
__________________
11y = -55 (See how the 4x - 4x eliminated the "x" variables?)
y = -5 (divide both sides by 11 to isolate the "y")

So nowwwww you know that y = -5. You can put that info into the first equation. Let's do that below:

4x - y = 9 (original equation)
(see how the -5 was put in place of the "y" variable?)
4x + 5 = 9
4x = 4 (subtract 5 from both sides of the equation)
x = 1 (divide both sides by 4 to isolate the "x")

SO now you know that "x" is equal to 1 and
"y" is equal to -5.

Let's put those both in to the original equations and see if the info is true:

4x-y=9 (first original equation)

4 + 5 = 9
9 = 9 Yay! The solution works. Now let's try the 2nd equation.

x-3y=16 (2nd original equation)
1 - 3(-5) = 16

1 + 15 = 16
16 = 16 Yay! The solution works here, too.

I hope this helps! :-)

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