`2x + y - 3z = 10, y + z = 12, z = 2` Use back substitution to solve the system of equations.

Expert Answers

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EQ1:  `2x+y-3z=10`

EQ2:  `y+z=12`

EQ3:  `z=2`

In this system of equations,  the value of variable z is known. So to get the values of the variables substitute z=2 to one of the equations. It is better if it is plug-in to the second equation since it composed of two variables only.

y + z=12

y+2=12

Then, solve for y.

y=12-2

y=10

Now that the values of y and z are known, solve for x. Plug-in them to the first equation.

`2x+y-3z = 10`

`2x+10-3(2)=10`

`2x+10-6=10`

`2x+4=10`

`2x=10-4`

`2x=6`

`x=6/2`

`x=3`

Therefore, the solution is (3,10,2).

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