SOLUTION: Solve the following system of equations for the unknown variables.
2x + y = 17
y + z = 6
x – z = 7
Algebra.Com
Question 143829: Solve the following system of equations for the unknown variables.
2x + y = 17
y + z = 6
x – z = 7
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the third equation
Solve for z
Go to the 2nd equation
Plug in
Add 7 to both sides
Rearrange the terms
So we now have the system
Let's use substitution to solve this system
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
Start with the first equation
Subtract from both sides
Rearrange the equation
Divide both sides by
Break up the fraction
Reduce
---------------------
Since , we can now replace each in the second equation with to solve for
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Combine like terms on the left side
Subtract 17 from both sides
Combine like terms on the right side
Divide both sides by -1 to isolate x
Divide
So the first part of our answer is:
Since we know that we can plug it into the equation (remember we previously solved for in the first equation).
Start with the equation where was previously isolated.
Plug in
Multiply
Combine like terms
So the second part of our answer is:
Go back to the third equation
Plug in
Subtract 4 from both sides
Combine like terms on the right side
Divide both sides by -1 to isolate z
Divide
So the third part of our answer is:
-----------------Summary------------------------------
So our answers are:
, , and
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