7. Systems of Equations & Matrices

In Exercises 19–22, find the quadratic function y = ax²+bx+c whose graph passes through the given points. (−1,−4), (1,−2), (2, 5)

In Exercises 19–22, 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. 3(2x+y)+5z=−1, 2(x−3y+4z)=−9, 4(1+x)=−3(z−3y)

Solve each system in Exercises 5–18. x+y=−4, y−z=1, 2x+y+3z=−21

Solve each system in Exercises 5–18. 2x+y=2, x+y−z=4, 3x+2y+z=0

Solve each system in Exercises 5–18. 2x−4y+3z=17, x+2y−z=0, 4x−y−z=6

Solve each system in Exercises 5–18. 3x+2y−3z=−2, 2x−5y+2z=−2, 4x−3y+4z= 10

Solve each system in Exercises 5–18. 4x−0y+2z=11, x+2y−z=−1, 2x+2y−3z=−1

Solve each system in Exercises 5–18. x+0y+2z=11, x+0y+3z=14, x+2y−0z=5

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (4, 1, 2) x−2y=2, 2x+3y=11, y−4z=−7

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (2,−1, 3) x+ y+0z=4, x−2y−0z=1, 2x−y−2z=−1

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)