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Please help! Solve the system!!!! Show work as well pls

Please help! Solve the system!!!! Show work as well pls-example-1

1 Answer

6 votes

Answer:

(x, y, z) = (2, -1, 5)

Explanation:

You want the solution to the system of equations ...

  • 2x +y +z = 8
  • x +2y -z = -5
  • z = 2x -y

Solution

The last equation gives an expression for z that can be substituted into the first two equations.

2x +y +(2x -y) = 8 ⇒ 4x = 8

x +2y -(2x -y) = -5 ⇒ -x +3y = -5

The first of these reduced equations is easily solve for x:

x = 8/4 = 2

Using that in the second of the reduced equations, we have ...

-2 +3y = -5

3y = -3 . . . . . . . . add 2

y = -1 . . . . . . . divide by 3

Now, we can find z:

z = 2x -y = 2(2) -(-1) = 5

The solution is (x, y, z) = (2, -1, 5).

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Additional comment

While we can always write the system of equations as an augmented matrix and ask a calculator to solve it (see attachment), it can be just as easy to take a look at the equations and develop a strategy. The given expression for z (3rd equation) makes substitution a good solution strategy. As it happens, x is developed right away by substituting for z in the first equation.

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Please help! Solve the system!!!! Show work as well pls-example-1
User TantanQi
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