Graphing and Solving Systems of Linear Equations in Two Variables

Problem: 1

Use a three–dimensional coordinate system to plot the ordered triple.

(3, –1, –5)

Problem: 3

Is (1, 3, –2) a solution of the system?

4a + 8b – 5c = 20

3a – 9b – 2c = 34

5a –2b + 2c = –5

Problem: 5

Graph: 2x – y – 3z = 6.

Problem: 7

Graph: 40x + 100y + 50z = 200.

Problem: 9

Rewrite the linear equation as a function of x and y. Then find the value of the function for the given values.

–3x – 8y + 8z = 16

Problem: 11

Find the value of r, s, t.

Problem: 13

Use the method of substitution to solve the system of equations:

3x – y + 3z = 6

2y + z = 8

z = 2

Problem: 15

Solve the system.

x + y – 2z = 8

y + z = 9

z = –1

Problem: 17

Solve the system.

3x –y – z = 4

x – 3y + z = –8

–3x – 3y + z = –4

Problem: 19

Find the value of x, y, z.

Problem: 21

Solve the system.

3x + 2y = 3 + z

x – 3y= 2 – 2z

4x + 3y = 1 + 3z

Problem: 23

Solve the system.

Problem: 25

Show that the following system is inconsistent.

Problem: 27

Solve the system using the substitution method.

x– 9y – z = –12

–x + 8y + 2z = 8

4x– 2y – 6z = 24

Problem: 29

Use elimination to solve:

Problem: 31

Use elimination to solve:

Problem: 33

Solve the system using linear combination method.

x+ 3y + 5z = –2

3x– y + z = 2

4x + 6y – 6z = 32

Problem: 35

Solve the system using any algebraic method.

20x – y + 8z = –20

x+ y – 6z = 12

4x– 3y – 24z = 48

Problem: 37

Find the value of a, b, and c.

Problem: 39

Solve if possible:

If not, state whether the system is inconsistent or dependent.

Problem: 41

Solve if possible:

If not, state whether the system is inconsistent or dependent.

Problem: 43

Is (1, 3, –2) a solution of the system?

4a + 8b – 5c = 20

3a – 9b – 2c = 34

5a –2b + 2c = –5

Problem: 45

Solve and verify.

3x + 7y + 2z = 3

3x + 8y – 4z = 1

9x + 21y + 4z = 7

Problem: 47

Find the three numbers.

Sum of the numbers = 10

First number = Two times the second number

Sum of the first and the third number = 6

Problem: 1

Use a three–dimensional coordinate system to plot the ordered triple.

(3, –1, –5)

Problem: 3

Is (1, 3, –2) a solution of the system?

4a + 8b – 5c = 20

3a – 9b – 2c = 34

5a –2b + 2c = –5

Problem: 5

Graph: 2x – y – 3z = 6.

Problem: 7

Graph: 40x + 100y + 50z = 200.

Problem: 9

Rewrite the linear equation as a function of x and y. Then find the value of the function for the given values.

–3x – 8y + 8z = 16

Problem: 11

Find the value of r, s, t.

Problem: 13

Use the method of substitution to solve the system of equations:

3x – y + 3z = 6

2y + z = 8

z = 2

Problem: 15

Solve the system.

x + y – 2z = 8

y + z = 9

z = –1

Problem: 17

Solve the system.

3x – y – z = 4

x – 3y + z = –8

–3x – 3y + z = –4

Problem: 19

Find the value of x, y, z.

Problem: 21

Solve the system.

3x + 2y = 3 + z

x – 3y = 2 – 2z

4x + 3y = 1 + 3z

Problem: 23

Solve the system.

Problem: 25

Show that the following system is inconsistent.

Problem: 27

Solve the system using the substitution method.

x – 9y – z = –12

–x + 8y + 2z = 8

4x– 2y – 6z = 24

Problem: 29

Use elimination to solve:

Problem: 31

Use elimination to solve:

Problem: 33

Solve the system using linear combination method.

x + 3y + 5z = –2

3x– y + z = 2

4x + 6y – 6z = 32

Problem: 35

Solve the system using any algebraic method.

20x – y + 8z = –20

x + y – 6z = 12

4x– 3y – 24z = 48

Problem: 37

Find the value of a, b, and c.

Problem: 39

Solve if possible:

If not, state whether the system is inconsistent or dependent.

Problem: 41

Solve if possible:

If not, state whether the system is inconsistent or dependent.

Problem: 43

Is (1, 3, –2) a solution of the system?

4a + 8b – 5c = 20

3a – 9b – 2c = 34

5a –2b + 2c = –5

Problem: 45

Solve and verify.

3x + 7y + 2z = 3

3x + 8y – 4z = 1

9x + 21y + 4z = 7

Problem: 47

Find the three numbers.

Sum of the numbers = 10

First number = Two times the second number

Sum of the first and the third number = 6

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