Question

Find the equation of the line through the intersection of the 3x -4y +1=0, 5x+y-1=0 which cuts off equal intercepts on the axes.

Answer 1

Answer:

the equation of the line through the intersection of the 3x -4y +1=0, 5x+y-1=0 which cuts off equal intercepts on the axes is 2x + 5y = 2

Step-by-step explanation:

We need to get the coordinates of the point of intersection of the two lines.

To get this, we solve the equations simultaneously.

3x - 4y + 1 = 0 ................i)

5x + y - 1 = 0 ..................ii)

Rewriting the two equations we have:

3x - 4y = -1 .....................i)

5x + y = 1 .....................ii)

We multiply equation ii with 4 to get:

3x - 4y = -1 ..................iii)

20x + 4y = 4 ................iv)

Adding the two equations we have:

23x = 3

x = 3/23

Substituting in i we have:

9/23 - 4y = -1

-4y = -32/23

y = 32/23 × 4

y = 8/23

The point of intersection (3/23, 8/23)

The line passing through this point will be:

3x - 4y + 1 = 5X + y - 1

Collecting the like terms together:

3x - 5x - 4y - y = -1 - 1

-2x - 5y = -2

Divide all through by -1

2x + 5y = 2