Solving system of equations

Graphing

100

Graph the equations to find the solution

y = x - 4

y = 3x - 6

(1, -3)

200

Graph the equations to find the solution

y = 3x + 1

y = -2x + 6

(1, 4)

Elimination

100

u + 6y = 32

u + 3y =17

y = 5

u = 2

200

4y +6x = 18

4y +2x = 6

x = 3

y = 0

300

-2y + 3x = 4

2y + 2x = 6

x = 2

y = 1

400

6x - 2y = 10

-6x + 3y = -9

y = 1

x = 2

Multiplying, then elimination

100

2a + 2x = 18

a + 3x = 17

a = 5

x = 4

200

3a + 5u = 17

2a + u = 9

a = 4

u = 1

300

x + 4y = 3

-3x + 3y = 6

y = 1 

x = -1

400

2x + 2y = 8

x + 3y = 10

y = 3

x = 1

Substitution

100

3a + 2v = 17

v = 7 - a

a = 3

v = 4

200

3a + 5c = 27

a = 7 - c

c = 3

a = 4

300

6c + 6z = 18

c = 5 - 2z

z = 2

c = 1

400

5u + v = 23

u = -6v + 22

v = 3

u = 4

One step, then substitution

100

2b + c = 12

2b = 10

b = 5

c = 2

200

2x + 6z = 14

5x = 5

x = 1

z = 2

300

a + 4x = 11

6a = 18

a = 3

x = 2

400

6b + 4v = 14

5b = 5

b = 1

v = 2