The graphs of the lines 3x + 4y = 2, 5x - y = 11 and x + ky = -2 all contain the same point.

Question

how do you work this.

Answer 1

Given equations are 3x+4y = 2

5x-y = 11

x+ky = -2

Write the equations in to slope intercept form.

y = (-3/4)x+1/2

y = 5x+11

y = (-x/k)-2

Graph

Draw the coordinate plane.

Graph the lines.

Observe the two lines 3x+4y = 2 and 5x-y = 11 are intersecting at (2,-1).

Given that three lines containing same point.

So x+ky = -2 line also intersect them at (2,-1).

x = 2, y = -1 is solution of three lines.

Plug the x,y values in x+ky = -2.

2-k = -2

Subtract 2 from each side.

-k = -4

Cancell the signs.

k = 4

So the requird equation is x+4y = -2.