Solving Systems of Equations by Substitution

label Algebra
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x+y-3z=-1

y=z

-x+2y=1

Oct 27th, 2015

Thank you for the opportunity to help you with your question!

To solve a system of equations by substitution means to replace a variable with what is equals. So, if y=z, we can replace all y's in the other equations with what y equals. All y's become "z" since y=z.

Now we have:

x+ z -3z =-1

-x+ 2z = 1.

It is best to simplify before doing the next step. Add together z and -3z.

x - 2z = -1

-x +2z =1.

Now we do the same step again. We will replace "x" with whatever "x" equals. We have to get x by itself in order to do this step. 

x - 2z (+2z) = -1 (+2z)

x= -1 +2z

Now we can replace x with what x equals, in the other equation. Anytime you see an "x", put (-1 +2z) in that spot.

-x +2z =1

-- (-1 +2z) +2z =1    (HINT: do not forget about the negative that was in front of x. We have to distribute)

1 -2z +2z = 1

1=1 WHEN THE VARIABLE DISAPPEARS IN THE ANSWER AND BOTH SIDES EQUAL EACH OTHER, THE ANSWER IS "ALL REAL NUMBERS".

so x, y, and z = all real answers

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 27th, 2015

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