Solve by Substitution x-2y+3z=7 , 2x+y+z=4 , -3x+2y-2z=-10

Problem

{[x−2*y+3*z=7],[2*x+y+z=4],[−3*x+2*y−2*z=−10])

Solution

1. Isolate the variable x in the first equation.

x=2*y−3*z+7

2. Substitute the expression for x into the second equation.

2*(2*y−3*z+7)+y+z=4

3. Simplify the second equation to find a relationship between y and z

4*y−6*z+14+y+z=4

5*y−5*z=−10

y−z=−2

y=z−2

4. Substitute the expressions for x and y into the third equation.

−3*(2*y−3*z+7)+2*y−2*z=−10

−6*y+9*z−21+2*y−2*z=−10

−4*y+7*z=11

5. Substitute y=z−2 into the simplified third equation to solve for z

−4*(z−2)+7*z=11

−4*z+8+7*z=11

3*z=3

z=1

6. Substitute z=1 back into the equation for y

y=1−2

y=−1

7. Substitute y=−1 and z=1 back into the equation for x

x=2*(−1)−3*(1)+7

x=−2−3+7

x=2

Final Answer

(x,y,z)=(2,−1,1)

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