Question

The lines represented by 3x + y - 12 = 0 and x - 3y + 6 = 0 intersects the y-axis
at
a) (0, - 2) and (0, 12)
c) (0, - 2) and (0, -12)
b) (0, 2) and (0, -12)
d) (0, 2) and (0,12)​

Answer 1

Answer:

c is the correct answer

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Answer 2

The correct answer is option d) (0, 2) and (0, 12)​.

Given:

The equations of two lines: 3x + y - 12 = 0 and x - 3y + 6 = 0.

To Find:

The point where these lines intersect the y-axis.

Solution:

The general equation of a lines is given by ax + by + c = 0.

Here, we have the equations of two lines:

3x + y - 12 = 0        ...................(I)

and x - 3y + 6 = 0          ...................(II)

We are asked to find the co-ordinates where these lines meet the y-axis.

When these two equations meet the y-axis, their x co-ordinate is 0.

So we substitute x = 0 in each of the given equations to find their respective x co-ordinates.

On substituting x = 0 in equation (I) we have:

3(0) + y - 12 = 0

⇒ y = 12.

∴ The line 3x + y - 12 = 0 meets the y-axis at (0, 12).

On substituting x = 0 in equation (II) we have:

0 - 3y + 6 = 0

⇒ 3y = 6

⇒ y = 2

∴ The line x - 3y + 6 = 0 meets the y-axis at (0, 2).

Hence, correct answer is option d) (0, 2) and (0, 12)​.

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