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\(\end{cases}\)$