Question

Can anyone tell me how to solve a linear equation in three variables with example

Answer 1

To use elimination to solve a system of three equations with three variables, follow this procedure:

Write all the equations in standard form cleared of decimals or fractions.

Choose a variable to eliminate; then choose any two of the three equations and eliminate the chosen variable.

Select a different set of two equations and eliminate the same variable as in Step 2.

Solve the two equations from steps 2 and 3 for the two variables they contain.

Substitute the answers from Step 4 into any equation involving the remaining variable.

Check the solution with all three original equations.

Example 1

Solve this system of equations using elimination.

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All the equations are already in the required form.

Choose a variable to eliminate, say x, and select two equations with which to eliminate it, say equations (1) and (2).

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Select a different set of two equations, say equations (2) and (3), and eliminate the same variable.

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Solve the system created by equations (4) and (5).

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Now, substitute z = 3 into equation (4) to find y.

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Use the answers from Step 4 and substitute into any equation involving the remaining variable.

Using equation (2), equation

Check the solution in all three original equations.

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The solution is x = –1, y = 2, z = 3.

Example 2

Solve this system of equations using the elimination method.

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Write all equations in standard form.

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Notice that equation (1) already has the y eliminated. Therefore, use equations (2) and (3) to eliminate y. Then use this result, together with equation (1), to solve for x and z. Use these results and substitute into either equation (2) or (3) to find y.

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Substitute z = 3 into equation (1).

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Substitute x = 4 and z = 3 into equation (2).

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Use the original equations to check the solution (the check is left to you).

The solution is x = 4, y = –2, z = 3.

Answer 2

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***1- elimination

1)Write all the equations in standard form cleared of decimals or fractions.

2)Choose a variable to eliminate; then choose any two of the three equations and eliminate the chosen variable.

3)Select a different set of two equations and eliminate the same variable as in Step 2)

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*****2:-

there are Matrix method too...

**"3- substitution method