Answer:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
Step-by-step explanation:
we are given three equation of variable x, y and z.
-3x-4y-3z= -7 ------------- (1)
2x-6y+z=3 ------------- (2)
5x-2y+5z=9 ------------- (3)
- Using elimination method to eliminate z from equation (1) and (2)
Make the coefficient of z same in both equation.
Multiply equation (2) by 3
-3x - 4y - 3z = -7
6x - 18y + 3z = 9
Add above equation to eliminate z
3x - 22y = 2 ---------------(4)
- Using elimination method to eliminate z from equation (2) and (3)
Make the coefficient of z same in both equation.
Multiply equation (2) by -5
-10x + 30y - 5z = -15
5x - 2y + 5z = 9
Add above equation to eliminate z
-5x + 28y = -6 ---------------(5)
- Using elimination method to eliminate x from equation (4) and (5)
Make the coefficient of x same in both equation.
Multiply equation (4) by 5 and equation (5) by 3
15x - 110y = 10
-15x + 84y = -18
Add above equation to eliminate x
-26y = -8
[tex]y=\dfrac{4}{13}[/tex]
Substitute y into equation (5) to get x
So, [tex]-5x+28(\frac{4}{13})=-6[/tex]
[tex]x=\dfrac{38}{13}[/tex]
Substitute x and y into equation (1)
[tex]-3\cdot \frac{38}{13}-4\cdot \frac{4}{13}-3z=-7[/tex]
[tex]z=-1[/tex]
Solution:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
