How many solutions?

To find the number of solutions for the system of equations given by and , we can set the two equations equal to each other:

By simplifying, we can solve for :

Now substitute back into one of the original equations to find :

Using :

Thus, the solution pair is , indicating that the system of equations has exactly one unique solution!

Now, if you graph these lines, you’ll see they intersect at only one point, confirming that there is one solution!

To double-check equation systems, it’s always helpful to look for parallel lines, which indicate no solutions, or identical lines, which suggest infinite solutions. Keep a close eye on the coefficients of when comparing equations!