7. Systems of Equations & Matrices

Solve by eliminating variables:

Solve each system in Exercises 25–26. $\begin{cases}\frac{x + 3}{2} - \frac{y - 1}{2} + \frac{z + 2}{4} = \frac{3}{2} \\\frac{x - 5}{2} + \frac{y + 1}{3} - \frac{z}{4} = - \frac{25}{6} \\\frac{x - 3}{4} - \frac{y + 1}{2} + \frac{z - 3}{2} = - \frac{5}{2}\end{cases}$

Solve each system in Exercises 25–26. $\begin{cases}\frac{x + 2}{6} - \frac{y + 4}{3} + \frac{z}{2} = 0 \\\frac{x + 1}{2} + \frac{y - 1}{2} - \frac{z}{4} = \frac{9}{2} \\\frac{x - 5}{4} + \frac{y + 1}{3} + \frac{z - 2}{2} = \frac{19}{4}\end{cases}$

Exercises 57–59 will help you prepare for the material covered in the next section. Solve: $\begin{cases}A + B = 3 \\2A - 2B + C = 17 \\4A - 2C = 14\end{cases}$

Find the quadratic function y = ax²+bx+c whose graph passes through the given points. (−1,−4), (1,−2), (2, 5)

Find the quadratic function y = ax²+bx+c whose graph passes through the given points. (−1, 6), (1, 4), (2, 9)

Solve each system in Exercises 5–18. $\begin{cases}3(2x + y) + 5z = -1 \\2(x - 3y + 4z) = -9 \\4(1 + x) = -3(z - 3y)\end{cases}$

Solve each system in Exercises 5–18. $\begin{cases}x + y = -4 \\y - z = 1 \\2x + y + 3z = -21\end{cases}$

Solve each system in Exercises 5–18. $\begin{cases}2x + y = 2 \\x + y - z = 4 \\3x + 2y + z = 0\end{cases}$

Solve each system in Exercises 5–18. $\begin{cases}2x - 4y + 3z = 17 \\x + 2y - z = 0 \\4x - y - z = 6\end{cases}$

Solve each system in Exercises 5–18. $\begin{cases}3x + 2y - 3z = -2 \\2x - 5y + 2z = -2 \\4x - 3y + 4z = 10\end{cases}$

Solve each system in Exercises 5–18. $\begin{cases}4x - y + 2z = 11 \\x + 2y - z = -1 \\2x + 2y - 3z = -1\end{cases}$

Solve each system in Exercises 5–18.

$\begin{cases}x + y + 2z = 11 \\x + y + 3z = 14 \\x + 2y - z = 5\end{cases}$

Determine if the given ordered triple is a solution of the system. $(4,1,2)$

$\begin{cases}x - 2y = 2 \\2x + 3y = 11 \\y - 4z = -7\end{cases}$

Determine if the given ordered triple is a solution of the system. $(2,-1,3)$

$\begin{cases}x + y + z = 4 \\x - 2y - z = 1 \\2x - y - 2z = -1\end{cases}$