Question

Assertion (A): `8/x + 5y = 11, and 4/x + 3y = 5` have solution `(1/2, -1).`

Reason (R): `(1/2,-1)` satisfies both the equations.

Options

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true, but R is the incorrect reason for A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, and R is the correct reason for A.

Explanation:

Given equations:

`8/x + 5y = 11,`

`4/x + 3y = 5,`

Solving both the equations using `(x = 1/2, y = -1),`

(i) `8/x + 5y = 11`

= `8/(1/2) + 5(-1)`

= 8(2) − 5

= 16 − 5

∴ 11 = 11

(ii) `4/x + 3y = 5`

= `4/(1/2) + 3(-1)`

= 4(2) − 3

= 8 − 3

∴ 5 = 5

So, the point `(1/2, -1)` satisfies both equations.