Find the equation of the line passing through the point of intersection of the lines 2x + y = 5 and x - 2y = 5 and having y-intercept equal to .

Equation of the lines are ⇒ 2x + y = 5 ...(i) ⇒ x - 2y = 5 ...(ii) Multiplying (i) by 2, we get ⇒ 4x + 2y = 10 ....(iii) Adding (iii) and (ii) we get, ⇒ 4x + 2y + x - 2y = 10 + 5 ⇒ 5x = 15 ⇒ x = 3. Substituting the values of x in (i) ⇒ 2(3) + y = 5 ⇒ 6 + y = 5 ⇒ y = -1. ∴ Coordinates of point of intersection are (3, -1). Hence, line passes through (3, -1). So it will satisfy y = mx + c. ⇒ -1 = 3m + c Given, y-intercept is so, c = ⇒ -1 = 3m + ⇒ -7 = 21m - 3 ⇒ -7 + 3 = 21m ⇒ -4 = 21m ⇒ m = Putting value of m and c in y = mx + c, Hence, the equation of the line is 4x + 21y + 9 = 0.

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Mathematics

Find the equation of the line passing through the point of intersection of the lines 2x + y = 5 and x - 2y = 5 and having y-intercept equal to .

Straight Line Eq

Related Questions

If the points (1, 4), (3, -2) and (p, -5) lie on a line, find the value of p.

Find the inclination of the line joining the points P(4, 0) and Q(7, 3).

Write down the equation of a line parallel to x - 2y + 8 = 0 and passing through the point (1, 2).