Solve by Substitution 2x+2y-z=2 , x-3y+z=-28 , -x+y=4

Problem

{[2*x+2*y−z=2],[x−3*y+z=−28],[−x+y=4])

Solution

1. Solve for a variable in the third equation. Since −x+y=4 we can isolate y

y=x+4

2. Substitute the expression for y into the first and second equations to create a system of two equations with two variables (x and z.

2*x+2*(x+4)−z=2

x−3*(x+4)+z=−28

3. Simplify these two equations.

2*x+2*x+8−z=2⇒4*x−z=−6

x−3*x−12+z=−28⇒−2*x+z=−16

4. Solve for z in the simplified version of the first equation.

z=4*x+6

5. Substitute the expression for z into the simplified version of the second equation to find x

−2*x+(4*x+6)=−16

2*x+6=−16

2*x=−22

x=−11

6. Substitute the value of x back into the expressions for y and z

y=−11+4=−7

z=4*(−11)+6=−44+6=−38

Final Answer

(x,y,z)=(−11,−7,−38)

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