Answer:
Therefore, x = 0 , y = 2 ,z = 5.
Explanation:
Given : Equations .
To find : What is the solution to the following system.
Solution : We have given that
x + 2y + z = 9 ------(1)
x -y + 3z = 13 ------(2)
2z = 10 ------(3)
On dividing by 2 both side on equation 3
z = 5 .
Plug the value z = 5 in equation (1 )and (2).
x + 2y + 5 = 9
On subtracting both sides by 5
x + 2y = 9 -5
x + 2y = 4 -------equation(3)
From equation 2
x - y + 3 (5) = 13
x - y + 15 = 13
On subtracting both sides by 15
x -y = -2 ------equation (4)
On subtracting equation(4) from equation(3).
x + 2y = 4
(-)x - ( +)y = - (+) 2
______________
0 + 3y = 6
On dividing by 3
y = 2.
Plug y = 2 in equation 3
x + 2( 2 ) = 4
x + 4 = 4.
On subtracting both sides by 2.
x = 4 - 4
x = 0 .
Therefore, x = 0 , y = 2 ,z = 5.