### Home > INT3 > Chapter 11 > Lesson 11.2.4 > Problem 11-100

Solve the system of equations below and then check your solution in each equation. Be sure to keep your work well organized. Homework Help ✎

*x*– 2*y*+ 3*z*= 8

2*x*+*y + z*= 6

*x*+*y + 2z*= 12

Choose a variable to eliminate and two equations to work with.

There are many possibilities.

We will use the first and third equations and eliminate *x* in the example.

Multiply the third equation by −1 then add it to the first.

Choose a different pair of equations and eliminate the same variable.

Here, we use the second and third equations.

Multiply the third equation by −2 then add it to the second.

Now combine the two result equations.

*x* − 2*y* + 3*z* = 8

−*x* − *y* − 2*z* = −12

−3*y* + *z* = −4

2*x* + *y* + *z* = 6

−2*x* − 2*y* − 4*z* = −24

−*y* − 3*z* = −18

−3*y* + *z* = −4

3*y* + 9*z* = 54

Solve for *z* and substitute to find the other values.

Check your result in each equation.