Question

Find the equation of the line through the intersection of lines 2x+3y=1 and 3x+4y=6 and perpendicular to 5x-2y=7

Answer 1

Solution :

Since the required line is perpendicular to the line 5x - 2y = 7, we consider it as

2x + 5y = k .....(i)

The two given intersecting lines are

• 2x + 3y = 1 .....(ii)
• 3x + 4y = 6 .....(iii)

Multiplying (ii) by 3 and (iii) by 2, we get

• 6x + 9y = 3
• 6x + 8y = 12

On subtraction, we get y = - 9

Putting y = - 9 in (ii), we get

2x + 3 (- 9) = 1

or, 2x - 27 = 1

or, 2x = 1 + 27 = 28

or, x = 14

Therefore, the point of intersection of lines (ii) and (iii) is (14, - 9)

Given that, (i) passes through the point (14, - 9), then

2 (14) + 5 (- 9) = k

or, 28 - 45 = k

or, k = - 17

Putting k = - 17 in (i) no. equation, we get the required line as

2x + 5y = - 17

i.e., 2x + 5y + 17 = 0

Answer 2

answer for this question is 2x+5y+17=0

hope its helpful

mark as brainlist