Systems of Linear Equations in 3 Variables Practice Problems

Find the solution using the elimination method. 

Solve the given three-variable equation system:

Solve the given three-variable equation system:

Work out the values of A, B, and C.

A + B = 2
5A + 8B - C = 1
6A - 3C = 0

If a quadratic function's (y = ax² + bx + c) graph passes through the given points (-1, 7), (1, 11), and (-2, 29), find the quadratic function.

If a quadratic function's (y = ax² + bx + c) graph passes through the given points (2, 3), (-1, 1), and (1, 2), find the quadratic function.

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system: 

Find out whether the given ordered triple satisfies the system of equations shown. 

(3, 1, 7) 

Find out whether the given ordered triple satisfies the system of equations shown.
(1, −1, 2) 

Determine the coefficient of x², x and the constant R in the given function y = Px²+Qx+R, which passes through (-3, 0), (0, 3), and (1, 0)

Solve the given system of equation 

x + y + z = 3

3x + y - 2z = 6

x -2y - z = 3

In a triangle ABC, the measure of the smallest angle is 20° less than the measure of the medium angle and the measure of the largest angle is 50° less than thrice the measure of the medium angle. Find all three angles of the triangle.

Solve the given system of linear equations.

Determine the quantity of each type of ball purchased by a sports teacher who bought a total of 40 balls. The number of basketballs exceeds the number of footballs by 8. Given that the cost of a tennis ball is $4, a basketball is $5, and a football is $7, the total cost of the purchase was $184.

The manufacturer of cement plans to produce 500 kg of cement and sell it for $5.00 per kg. She intends to mix three grades of cement with different prices - $10.00, $8.00, and $4.00 per kg. She must use three times more of the $4.00 cement than the $8.00 cement. What amount of each grade should she mix?