Solve the system x + 3y + 2z = -1, x - 2y + z = -2, 3x - y + 2z = -7. What is the value of z?

Solving $x^2+y^2=22$ and $y=x^2-2$, a student substitutes $x^2=y+2$, gets $y^2+y-20=0$, finds y = 4 and y = -5, and reports four solution points. What is wrong?

A farm makes a crates of apples and p crates of pears. Each of the crates of apples uses 4 units of material, each of the crates of pears uses 5, 60 units are available, and at most 15 crates of apples can be made. Which pair of constraints states this?

Solve the system 2x - y + z = -1, x - y + 2z = -5, 3x + y - z = 11. What is the solution as an ordered triple (x, y, z)?

Solve the system $y=x^2-2x+7$ and y = 2x + 4. Give the solutions as ordered pairs.

Solve the system $x^2+y^2=225$ and y = x - 3. Give the solutions as ordered pairs.

How many real solutions does the system $y=x^2-5x+6$ and y = 2x + 3 have?

Solve the system $y=x^2+x+4$ and y = 2x + 4. Give the solutions as ordered pairs.

For the system (1) x + y + z = 3, (2) x + 2y - z = 2, (3) x - y + 2z = 2, which pair of equations eliminates y when the two are added as written?

Solve the system $y=x^2+7x+5$ and y = 3x + 2. Give the solutions as ordered pairs.

A feasible region has vertices (0, 0), (0, 5), (4, 3), (6, 0). What is the minimum value of C = 5x + 3y over the region?

A ball's height in feet is $h=-16t^2+64t$, and a camera drone hovers at a height of 60 feet. At what times t, in seconds, is the ball level with the drone?

Solve the system x + y + z = 1, 3x + y - z = -3, x - 2y + z = 4. What is the value of x?

A theater sold 400 tickets for $4000. Adult tickets cost $15, student tickets $10 and child tickets $5, and twice as many student tickets sold as child tickets. Which system models this, with a, s and c the counts?

Solving $x^2+y^2=32$ and $y=x^2-2$, a student substitutes $x^2=y+2$, gets $y^2+y-30=0$, finds y = 5 and y = -6, and reports four solution points. What is wrong?

Solve the system x + 2y - z = 0, 2x + y + 3z = -9, x - 2y + z = 2. What is the solution as an ordered triple (x, y, z)?

Solve the system x + y + z = 3, 2x - y + z = -2, 2x + 2y - z = 9. What is the solution as an ordered triple (x, y, z)?

A feasible region has vertices (0, 0), (0, 7), (2, 6), (5, 2). What is the maximum value of P = 2x + y over the region?

Substituting to solve $y=x^2+5x+6$ and y = -2x - 6 gives one quadratic equation set equal to zero. Which equation is it?

A ball's height in feet is $h=-16t^2+32t$, and a camera drone hovers at a height of 12 feet. At what times t, in seconds, is the ball level with the drone?