# Simultaneous Equations

### 2x+y = 7 and x - y = 2

Compare the two equations.  What can we do to eliminate one of the variables?

2x + y = 7

x - y = 2

3x       = 9

x = 3

Substitute x into 2x + y = 7

2(3) + y = 7

6 + y = 7

y = 1

### 2x + y = 5 and x + y = 1

Compare the two equations.  What can we do to eliminate one of the variables?

Flip the second equation and compare the equations again.

2x + y = 5

-x - y = -1

x  = 4

Substitute x into 2x + y = 5

2(4) + y = 5

8 + y = 5

y = -3

### Solve 2x + y = 1 and x + y = -2

Compare the two equations.  What can we do to eliminate one of the variables?

Flip the second equation and compare the equations again.

2x + y = 1

-x  - y  = 2

x = 3

Substitute x into 2x + y = 1

2(3) + y = 1

6 + y = 1

y = -5

### Solve 2x – y = 1 and x – y = -2

Compare the two equations.  What can we do to eliminate one of the variables?

Flip the second equation

2x - y = 1

-x + y = 2

x           = 3

Substitute x into 2x - y = 1

2(3) - y = 1

6 - y = 1

y = 5