Systems of Equations Exercises

Example 1

Solve this system of equations using Gaussian Elimination.

2x + y – 3z = -10
-2y + z = -2
z = 6

Hint

This is already in triangular form. Substitute the z into Row 2 and solve for y. Then substitute the y and z into Row 1 to find the x.

Example 2

Solve this system of equations using Gaussian Elimination.

3x + 4y – z = -6
-2y + 10z = -8
4y – 2z = -2

Hint

This is almost in triangular form. Try multiplying Row 2 by 2, then adding that to Row 3.

Example 3

Solve this system of equations using Gaussian Elimination.

-7x – 3y + 3z = 12
2x + 2y + 2z = 0
-x – 4y + 3z = -9

Hint

Get this system in triangular form. Try multiplying Row 3 by 2, then add that to Row 2. Follow this by multiplying Row 3 by -7, then adding that to Row 1. Rewrite the original Row 1 and the two new equations. One more step to get it to triangular form. Can you do it?

Example 4

Solve this system of equations using Gaussian Elimination.

x – y – z = 4
2x – 2y – 2z = 8
5x – 5y – 5z = 20

Hint

Do you notice anything yet? If not, try multiplying Row 1 by -2, then add Row 1 and Row 2.

Example 5

Solve this system of equations using Gaussian Elimination.

x + y + z = 0
-x – y + 3z = 3
-x – y – z = 2

Hint

Add Row 1 and Row 2 and a clue will be revealed.

Systems of Equations Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

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