Question

How many soulutions does the following system have?

y=1/2x + 3 .
2y - x = 6 .

Answer 1

Infinite number of solutions

Step-by step explanation:

Given system of equations are

`y=(1)/(2) x+3` – – – – (1)

2y – x = 6 – – – – (2)

Equation (1) can be written as

⇒
`y=(1)/(2) x+3`

Take LCM on both sides of the equation.

⇒
`(2)/(2) y=(1)/(2) x+(6)/(2)`

⇒ 2y = x + 6

⇒ x – 2y + 6 = 0 – – – – (3)

Equation (2) can be written as

⇒ 2y – x = 6

⇒ x – 2y + 6 = 0 – – – – (4)

`a_(1)=1, b_(1)=-2, c_(1)=6 \text { and } a_(2)=1, b_(2)=-2, c_(2)=6`

We know that the system of equations have infinite number of solutions if

`(a_(1))/(a_(2))=(b_(1))/(b_(2))=(c_(1))/(c_(2))`

⇒
`(1)/(1)=(-2)/(-2)=(6)/(6)`

Hence the given system have infinite number of solutions.