CPM Homework Help : INT3 Problem 12-10

Use the algebraic strategies you have developed to solve the system of equations below. Be sure to check your solution.

$2x + y - 3z = -12$
$5x - y + z = 11$
$x + 3y - 2z = -13$

Step 1:

Choose a pair of equations that can be added together to eliminate a variable.

$\left. \begin{array}{l}{ 2 x + y - 3 z = - 12 }\\{ + 5 x - y + z = 11 }\\\end{array} \right.$

${ 7 x \ \ \ \ \ \ \ \ \ \ - 2 z = - 1 }$

Step 2:

Choose a different pair of equations to add together to eliminate the same variable.
In this case, you will have to multiply each equation by a constant.

$\left. \begin{array}{l}{-3( 2 x + y - 3 z = - 12) }\\{ + \ \ \ \ \ x + 3y -2z = -13 }\\\end{array} \right.$

$-5x \ \ \ \ \ \ \ \ \ +7z=23$

Step 3:

Solve the system of equations you created in steps 1 and 2 for either $x$ or $z$ .

Step 4:

Solve for $x$ using the two-variable equation you created in either step 1 or step 2.
Then substitute the values for $x$ and $z$ into one of the original equations to solve for $y$ .

Hint:

Check your solution in a different equation than the one you used to solve for $y$ .