Math, asked by priyamganguli1, 16 days ago

) Find the equation of the line passing through the intersection of the lines

3x + 2y = 7 and x – y + 1 = 0 and parallel to 2x + y = 0.

Answers

Answered by amansharma264

Equation of lines passing through point of intersection.

⇒ 3x + 2y = 7. - - - - - (1).

⇒ x - y + 1 = 0. - - - - - (2).

Parallel to the line 2x + y = 0.

As we know that,

Solving equation (1) and (2), we get.

We can write equation (2) as,

⇒ x + 1 = y. - - - - - (2).

Put the value of equation (2) in equation (1), we get.

⇒ 3x + 2(x + 1) = 7.

⇒ 3x + 2x + 2 = 7.

⇒ 5x = 7 - 2.

⇒ 5x = 5.

⇒ x = 1.

Put the value of x = 1 in equation (2), we get.

⇒ y = x + 1.

⇒ y = 1 + 1.

⇒ y = 2

Values of (x, y) = (1, 2).

As we know that,

Slope of a parallel line : m = - a/b.

Slope of line : 2x + y = 0 ⇒ m = - 2.

As we know that,

Formula of equation of line.

⇒ (y - y₁) = m(x - x₁).

Put the values in the equation, we get.

⇒ (y - 2) = - 2(x - 1).

⇒ y - 2 = - 2x + 2.

⇒ y + 2x = 2 + 2.

⇒ 2x + y = 4.

Equation of line : 2x + y = 4.

Previous Question

Next Question