Solve each system of three linear equations containing three unknowns.?

Question

x-3y=12 
2y-3z=-9 
2x+z=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 2 and 3 that contain opposite coefficient of z - variable multiply the third equation by 3.

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

The resultant equation is taken as fourth equation : 6x + 2y = 12.

Solve the system of two equations with two variables.

To get two equations 1 and 4 that contain opposite coefficient of x - variable multiply the first equation by negative 6.

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

.

The resultant statement 20y = - 60 ------> y = - 3.

To find the value of x, substitute y = - 3 in the equation 1 : x - 3y = 12 and solve for x.

x - 3(- 3) = 12

x + 9 = 12

x = 3.

To find the value of z, substitute x = 3 in the equation 3 : 2x + z = 7 and solve for z.

2(3) + z = 7

6 + z = 7

z = 1.

The solution (x, y, z) = (3, - 3, 1).