Solve the following system of equations and show work.

Question

x−2y+ 3z = 9

−x+ 3y+ z = −2

2x−5y+5z =17?

Answer 1

The system of equations are .

Use the elimination method to make a system of two equations in two variables.

The two equations 1 and 2 contains opposite coefficient of x - variable.

Write the equations 1 and 2 in column form and add the corresponding columns to eliminate x - variable.

The resultant equation is taken as fourth equation : .

To get two equations 2 and 3 that contain opposite terms (x - variable) multiply the second equation by 2.

Write the equations 2 and 3 in column form and subtract the corresponding columns to eliminate x - variable.

The resultant equation is taken as fifth equation : .

Solve the system of two equations with two variables.

The two equations 4 and 5 contain same coefficient of y - variable.

Write the equations 4 and 5 in column form and subtract the corresponding columns to eliminate y - variable.

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The resultant equation is .

Use one of the equation with two variables (Equation : 4 or 5) to solve for y.

The fourth equation: .

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Solve for x using one of the original equations with three variables.

The first equation: .

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The solution .