Solve each system of equations.?

Question

2x-y+2z=1 
-2x+3y-2z=3 
4x-y+6z=7

Answer 1

The system of equations are .

Use the elimination method to make a system of two equations in two variables.

To get two equations 1 and 2 that contain opposite coefficient of y - variable multiply the first equation by 3.

Write the equations 1 and 2 in column form and add the corresponding columns to eliminate y - variable.

The resultant equation is taken as fourth equation : 4x + 4z = 6.

To get two equations 2 and 3 that contain opposite coefficient of y - variable multiply the third equation by 3.

Write the equations 2 and 3 in column form and add the corresponding columns to eliminate y - variable.

The resultant equation is taken as fifth equation : 10x + 16z = 24.

Solve the system of two equations with two variables.

To get two equations 4 and 5 that contain opposite coefficient of z - variable multiply the fourth equation by negative 4.

Write the equations 4 and 5 in column form and add the corresponding columns to eliminate z - variable.

The resultant statement - 6x = 0 ------> x = 0.

Use one of the equation with two variables (Equation: 4 or 5) to solve for z.

The fourth equation: 4x + 4z = 6.

4(0) + 4z = 6

4z = 6

z = 6/4 = 3/2.

Solve for y using one of the original equations with three variables.

The first equation: 2x - y + 2z = 1.

2(0) - y + 2(3/2) = 1

- y + 3 = 1

- y = - 2

y = 2.

The solution (x, y, z) = (0, 2, 3/2).