**Question 4. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:**

(i) x + y = 5, 2x + 2y = 10

Convert the equation in form of a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x+ b_{2}y + c_{2} = 0

We get

x + y -5 = 0, 2 x + 2 y -10 = 0

Compare the equation with

We get

a1 = 1, b1 = 1, and c1 = -5

a2 = 2 b2 = 2 and c2 = - 10

So we get

**Dependent and consistent so it will have many solutions .**

(ii) x – y = 8, 3x – 3y = 16

Convert the equation in form of

a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x+ b_{2}y + c_{2} = 0

We get

x – y -8 = , 3x – 3y -16 = 0

Compare the equation with

We get

a1 = 1, b1 = - 1, and c1 = - 8

a2 = 3 b2 = - 3 and c2 = - 16

So we get

**So both lines are Inconsistent**

(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0

Compare the equation with

We get

a1 = 2, b1 = 1, and c1 = - 6

a2 = 4 b2 = - 2 and c2 = - 4

So we get

**So both lines are consistent **

Solve the equations graphically

2x + y – 6 = 0,

Subtract 2x and add 6 both side we get

y = 6 – 2x

plug x = 1,2 and 3 we get

y = 6 - 2 * 1 = 4

y = 6 - 2 * 2 = 2

y = 6 - 2 * 3 = 0

4 x – 2 y – 4 = 0

Divide by 2 we get

2 x – y - 2 = 0

Add y both side we get

2 x – 2 = y

or

y = 2x – 2

plug x = 1.2 and 3 we get

y = 2 * 1 – 2 = 0

y = 2 * 2 – 2 = 2

y = 2 * 3 – 2 = 4

**Answer x = 2 and y = 2 **

(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

Compare the equation with

We get

a1 = 2, b1 = - 2, and c1 = - 2

a2 = 2 b2 = - 2 and c2 = - 5

So we get

**So both lines are Inconsistent**