Math CentralQuandaries & Queries


Subject: Business Calculus
Name: Mark
Who are you: Student

Find the points of intersection of the given pair of curves.

2x - 3y = -8 and 3x - 5y = -13

We have two responses for you.

Hi Mark.

This is two linear equations with two unknowns. To solve the problem, solve each equation for y on the left-hand-side ( y = some expression of x). Then the two right hand sides must be equal to each other, since they both equal y. So just write them down as equal to each other and solve for x. Once you have x, put its value into either one of the original equations and solve for y.

Hope this helps,
Stephen La Rocque.


Hi Mark,

First of all, you know since the exponent on the x's and y's is 1, your equations represent two lines, so at most there will be one intersection point (there would be none if the lines are parallel). So, if you find one intersection point, you don't have to worry that you missed another along the way somewhere!

Let's say the two lines intersect at the point (a,b) in the coordinate plane. Since this point is on both of the lines, the coordinates must satisfy the equations for both lines. That means:

2a - 3b = -8 and 3a - 5b = -13

To solve this system of two equations with two unknowns, you can use the first equation to solve for a (get an expression for a in terms of b), and then substitute this expression into the second equation where you see a.

Another method you can use is illustrated in this previous question:


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS