7. Systems of Equations & Matrices

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\(\end{cases}\)$

Find the quadratic function y = ax^2 + bx + c whose graph passes through the points (1, 4), (3, 20), and (-2, 25).

Solve each system in Exercises 12–13. The is a piecewise function

Solve each problem. See Examples 5 and 9. The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles.

Solve each problem. See Examples 5 and 9. Solve the system of equations (4), (5), and (6) from Example 9.

$25x+40y+20z=2200$ (4)

$4x+2y+3z=280$ (5)

$3x+2y+z=180$ (6)