Aline joins the point
is the point of intersection of 5x - 2y + 3 = 0 and 4x - 3y + 1 = 0 to
of intersection of x = y and x = 3y + 4.find the equation of the line.

Intersection of the first two lines:

Multiply the first equation by 4 and the second by 5:

Subtract the two equations:

Plug this value for y in one of the equation, for example the first:

So, the first point of intersection is

We can find the intersection of the other two lines in the same way: we start with

Use the fact that x and y are the same to rewrite the second equation as

And since x and y are the same, the second point is

So, we're looking for a line passing through and . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be

In the attached figure, line is light green, line is dark green, and their intersection is point A.

Simiarly, line is red, line is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

a

step-by-step explanation: