Answer:
[tex]x=34,y=-27andz=-1[/tex]
Step-by-step explanation:
Given:
[tex]2x+2y+6z=8[/tex] equation:1
[tex]5x+6y+5z=3[/tex] equation:2
[tex]5x+6y+3z=5[/tex] equation:3
We have to find the value of x,y and z
Eliminating two variables to find the value of third variable
Subtracting equation:2 from equation:3
[tex]5x+6y+3z-(5x+6y+5z)=5-3[/tex]
[tex]5x+6y+3z-5x-6y-5z=2\\-2z=2\\z=-1[/tex]
Solving the equation:1 for 'x'
[tex]2x+2y+6z=8[/tex]
[tex]2x=8-2y-6z\\2x=8-2y-6(-1)\\2x=8-2y+6\\2x=14-2y\\x=7-y[/tex]
Putting x and z in equation 2
[tex]5(7-y)+6y+5(-1)=3\\35-5y+6y-5=3\\y+30=3\\y=3-30\\y=-27[/tex]
Putting the value of 'y' and 'z' in equation:2 to find the value of 'x'
[tex]5x+6(-27)+5(-1)=3\\5x-162-5=3\\5x-167=3\\5x=3+167\\5x=170\\x=\frac{170}{5}\\ x=34[/tex]
The values of x,y and z are
[tex]x=34,y=-27andz=-1[/tex]
