Solve each system of equations

Question

2y-z=-3
-2x+3y=10
4x+3z=-11

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 2 and 3 that contain opposite coefficient of x - variable multiply the second equation by 2.

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

The resultant equation is taken as fourth equation : 6y +3z = 9.

Solve the system of two equations with two variables.

To get two equations 1 and 4 that contain opposite coefficient of z - variable multiply the first equation by 3.

Write the equations 1 and 4 in column form and add the corresponding columns to eliminate z - variable.

.

The resultant equation 12y = 0 ------> y = 0.

To find the value of z, substitute y = 0 in the equation 1 : 2y - z = - 3 and solve for x.

2(0) - z = - 3

- z = - 3

z = 3.

To find the value of x, substitute y = 0 in the equation 2 : - 2x + 3y = 10 and solve for x.

- 2x + 3(0) = 10

- 2x = 10

x = - 5.

The solution (x, y, z) = (- 5, 0, 3).