Question

find the point of intersection of the pair of lines: L: 2x-y= -4 M: 4x+3y=2.

Answer 1

The equations are 2x - y = - 4 and 4x + 3y = 2.

Write the equations in slope - intercept form y = mx + b, where m is slope and b is y - intercept.

The first equation is 2x - y = - 4.

y = 2x + 4.

Compare the equation with slope - intercept form y = mx + b.

slope = 2 and y - intercept is 4.

y - intercept is 4, so the line crosses the y - axis at (0, 4)

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, 4), move 2 units up and 1 unit right, then plot the point (1, 6).

The second equation is 4x + 3y = 2.

3y = - 4x + 2

Divide each side by 3.

y = (- 4/3)x + (2/3)

Compare the equation with slope-intercept form y = mx + b.

slope = - 4/3 and y - intercept is 2/3.

y - intercept is 2/3, so the line crosses the y - axis at (0, 2/3).

Using slope find the next point.

Slope = rise/run = - 4/3

Start at point (0, 2/3), move 4 units down and 3 units right, then plot the point (3, - 10/3).

Draw the lines through these points.

Graph :

The lines are intersect at a point, i.e, (x, y ) = (- 1, 2).