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Find the equation of a line formed by the two points P and Q. Where P is the intersection point of lines 6x – y = 1 and  x + y = 6. Where Q is the intersection point of lines 5x – 3y = -1 and 2x + 6y = -10?

Find the equation of a line formed by the two points P and Q. Where P is the intersection point of lines 6x – y = 1 and  x + y = 6. Where Q is the intersection point of lines 5x – 3y = -1 and 2x + 6y = -10? Correct Answer 7x - 2y + 3 = 0

Given:

Four equations are 6x – y = 1, x + y = 6, 5x – 3y = -1 and 2x + 6y = -10.

Formula Used:

Equation of a line passing from two points P(a, b) and Q(c, d)

⇒ Y – b = {(d – b)/(c – a )}(X – a )

Calculation:

Now, intersection point of lines 6x – y = 1 and x + y = 6 wil be

⇒ 6x – y = 1 ( Add the two equations)

     x  +  y = 6

      7x = 7

⇒ x = 1

By putting x = 1 in x + y = 6, we get y = 5

The point P will be (1, 5)      ----(1)

Now consider two equations 5x – 3y = -1 and 2x + 6y = -10

⇒ 5x – 3y = -1 (Multiply it by 2)

⇒ 10x – 6y = -2 (Add them)

     2x + 6y = -10

    12x = -12

⇒ x = -1

Put x in 2x + 6y = -10

We get y = -2

Point Q will be (-1, -2)      ----(2)

Now the equation of the line passing from point P(1, 5) and Q(-1, -2)

⇒ Y – 5 = {(-2 - 5)/(-1 - 1)}(X – 1)

⇒ 2(Y – 5) = 7(X – 1)

∴ The equation is 7X – 2Y + 3 = 0

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