# Inconsistent or dependent system of equations

Solve the system of linear equations. If the unique solution does not exist state weather the system is inconsistent or dependent.

1. -x - y = 4

x -y = -8

2. 3x - 2y = 23

x +5y = -15

3. 4x + 2y = 4

y = 2 - 2x

4. 4x - 3y = 9

2x + y = 12

5. 5x + 4y = 40

x + 2y = 11

#### Solution Preview

...= 23 -------------(i)

x +5y = -15 --------------(ii)

Multiply equation (ii) by 3, we will get

3x + 15y = -45 ----------(iii)

Subtract (i) from (iii), we will get

17y = -68

Divide each side by 17, we will get

y = -4

Substitute value of y in (ii), we will get

x + 5(-4) = -15

x - 20 = -15

=> x = -15 + 20 = 5

The solution is x = 5, y = -4

3. 4x + 2y = 4

y = 2 - 2x ...