Checkpoint: Solving Systems of Equations with Three Variables Solutions

Find the solution that will satisfy all three variables.

$A : x + y = - 1$

$A + B, solve for y . \begin{matrix} (x + y = - 1) (- 1) & \Rightarrow \end{matrix} \begin{matrix} \begin{array}{l} \begin{matrix} \end{matrix} \\ - x - y = 1 \\ + x + 2 y = 1 \end{array} \\ y = 2 \end{matrix}$

$B : x + 2 y = 1$

$\begin{array}{rcl} Solve for x . \\ x + (2) & = & - 1 \\ x & = & - 3 \end{array}$

$(- 3) + (2) = - 1 ✓ (- 3) + 2 (2) = 1 ✓$

$C : 2 x + 3 y + 4 z = 11$

$\begin{array}{rcl} Solve for z . \\ 2 (- 3) + 3 (2) + 4 z & = & 11 \\ - 6 + 6 + 4 z & = & 11 \\ 4 z & = & 11 \\ z & = & \frac{11}{4} \end{array}$

$solution (- 3, 2, \frac{11}{4})$

Note

This solution shows eliminating x to solve for y. You may also eliminate y first. The solution will remain the same.

Q: What equations will you combine first?
A: A and B.

Q: How will you know when you have finished a system of equations with three variables?
A: You have the value for each variable and the values make all the equations true.