Solve by Substitution z=3 , y-6x=8 , x=3y-5z

Problem

{[z=3],[y−6*x=8],[x=3*y−5*z])

Solution

1. Substitute the known value z=3 into the third equation to express x in terms of y

x=3*y−5*(3)

x=3*y−15

2. Substitute the expression for x into the second equation to solve for y

y−6*(3*y−15)=8

3. Distribute the constant −6 through the parentheses.

y−18*y+90=8

4. Combine like terms and isolate the variable y

−17*y+90=8

−17*y=8−90

−17*y=−82

y=82/17

5. Substitute the value of y back into the expression for x to find its numerical value.

x=3*(82/17)−15

x=246/17−255/17

x=−9/17

Final Answer

(x,y,z)=(−9/17,82/17,3)

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