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)