Question

Solve the system using substitution.

4x + y − 2z = 18
2x − 3y + 3z = 21
x − 3y = 6


The solution to the system of three linear equations is the ordered triple (x,y,z) .

Answer 1

Given: The following system:

4x + y − 2z=18 ......[1]

2x-3y+3z = 21 ......[2]

x-3y=6 ......[3]

we can write equation [3] as;

3y = x-6 ......[4]

Multiply by 3 in equation [1] to both sides of an equation we get,

`3 \cdot(4x+y-2z)= 3\cdot 18` or

12x+3y-6z=54 ......[5]

Substituting the equation [4] in [2] and [5] we get;

2x-(x-6)+3z=21 or

2x-x+6+3z=21

Simplify:

x+3z=15 .....[6] [combine like terms]

12x+x-6-6z =54

Simplify:

13x-6z=60 ......[7] [Combine like terms]

On Solving equation [6] and [7] simultaneously,

x+3z=15

13x-6z=60

we get the value of x

i.e, x=6

Substitute the value of x in equation x+3z=15 we get

6+3z=15 or

3z=9

Simplify:

z=3

Also, substitute the value of x=6 in equation [3] we get the value of y;

x-3y=6

6-3y=6 or

-3y = 0

Simplify:

y = 0

Therefore, the solution to the system of three linear equation is, (6, 0 , 3)