Find the area (in sq. units) bounded by lines 12x + 5y = 60, 3y - 4x = 36 and x-axis

To find the area bounded by the lines and the x-axis, we first need to find the points of intersection of the lines and the x-axis.

1. Set y = 0 in both equations to find the x-intercepts.

For 12x + 5y = 60, when y = 0, we get 12x = 60, so x = 60/12 = 5.

For 3y - 4x = 36, when y = 0, we get -4x = 36, so x = 36/-4 = -9.

2. Now, find the point of intersection of the two lines.

To do this, we can set the two equations equal to each other and solve for x.

12x + 5y = 3y - 4x

This simplifies to 16x = -2y, or y = -8x.

Substitute y = -8x into one of the original equations, say 12x + 5y = 60.

This gives 12x + 5(-8x) = 60, or -28x = 60, so x = 60/-28 = -15/7.

Substitute x = -15/7 into y = -8x to get y = -8(-15/7) = 120/7.

So, the point of intersection of the two lines is (-15/7, 120/7).

3. The area bounded by the lines and the x-axis is a trapezoid with bases 5 and -9 and height 120/7.

The area of a trapezoid is given by the formula 1/2 * (base1 + base2) * height.

So, the area is 1/2 * (5 - (-9)) * 120/7 = 1/2 * 14 * 120/7 = 120 square units.