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solve system of equations using substitution

label Algebra
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x + y=2

6x-2y=4                                                                                                                                                                

Nov 21st, 2014

Hello there,

You have the following equations: x + y = 2 and 6x - 2y = 4. When using the method of substitution, you must rearrange one equation and substitute that rearrangement into the other equation. In this case, let's change the first equation so that only one variable is on the left side of the equal sign and everything else is on the right side of the equal sign. So,

x + y = 2 --> x = 2 - y

Now we have

x = 2 - y

6x - 2y = 4

We can now substitute the first equation into the second equation to get

6x - 2y = 4

6(2 - y) - 2y = 4

12 - 6y - 2y = 4

12 - 8y = 4

-8y = 4 - 12

-8y = -8

y = 1

So we now have a value for y. Let's solve for the value of x by plugging in the value of y into one of the two original equations. I shall use the first one.

x + y = 2

x + 1 = 2

x = 2 - 1

x = 1

So now we have x = 1 and y = 1. Let's check the values by substituting them into the original equation.

First check,

x + y = 2

1 + 1 = 2

2 = 2 (yay)

Second check,

6x - 2y = 4

6(1) - 2(1) = 4

6 - 2 = 4

4 = 4 (yay)

So our solution is (1, 1).

Hope this helped. Stay strong and math on!

Nov 21st, 2014

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