Question

Solve for x, y, and z in the system of equations.

x + 7y + 3z = 29
3z + x - 2y = −7
5y = 10 - 2x

Answer 1

• x = -5
• y = 4
• z = 2

Explanation:

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

• x +7y +3z = 29
• x -2y +3z = -7
• 2x +5y = 10

Solution

The attachment shows a solution using the matrix functions of a calculator.

Ad hoc methods can also be used. Subtracting the second equation from the first gives ...

(x +7y +3z) -(x -2y +3z) = (29) -(-7)

9y = 36 . . . . . simplify

y = 4 . . . . . . divide by 9

Substituting this into the last equation, we have ...

2x +5(4) = 10

2x = -10 . . . . . . . subtract 20

x = -5 . . . . . . divide by 2

Using the second equation with these values, we have ...

-5 -2(4) +3z = -7

3z = 6 . . . . . . add 13

z = 2 . . . . . . divide by 2

The solution is (x, y, z) = (-5, 4, 2).

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