Find the solution to the system of equations.
2x - y + z = 3
x + 2y + z = 4
2x - y - 2z = 3
x = __, y = __, z = __

Question

Find the solution to the system of equations. 2x - y + z = 3 x + 2y + z = 4 2x - y - 2z = 3 x = __, y = __, z = __

SnapAndSolve AI · Accepted Answer

To solve the system of equations, we can use the elimination method.

Subtract Equation 3 from Equation 1:

(2x - y + z) - (2x - y - 2z) = 3 - 3

z + 2z = 0

3z = 0

z = 0

Substitute z = 0 into Equation 1:

2x - y + 0 = 3

2x - y = 3

Substitute z = 0 into Equation 2:

x + 2y + 0 = 4

x + 2y = 4

Now solve the two equations:

Multiply Equation 2 by 2:

2x + 4y = 8

Subtract Equation 1 from this result:

(2x + 4y) - (2x - y) = 8 - 3

5y = 5

y = 1

Substitute y = 1 into Equation 1:

2x - 1 = 3

2x = 4

x = 2

Thus, the solution is:

x = 2, y = 1, z = 0

Find the solution to the system of equations. 2x - y + z = 3 x + 2y + z = 4 2x - y - 2z = 3 x = , y = ,...