How many points of intersection do the equations 5x-3y equals -4 and x plus 2y equals 7 have?

Answer 1

These equations are both linear, so they will have either one point of intersection, zero points of intersection, or an infinite number of them. To answer this then, you can start by finding the slope of each line, and see if they are equal. If not, then the lines intersect at one point.

Starting with the first one:

5x - 3y = -4

∴ -3y = -5x - 4

∴ y = (5/3)x + 4/3

So this line has a slope of 5/3

And now for the second one:

x + 2y = 7

∴ 2y = 7 - x

∴ y = 7/2 - (1/2)x

So this line has a slope of 1/2.

The answer then is one. The two lines have two different slopes, and must therefore intersect at exactly one point.