Question

How many solutions are there for the following system of equations?

y = x² - 5x+3y = x-6
a) 1
b) 2
c) 3
d) 4

Answer 1

There are 2 solutions(option b) for the given system of equations.

Step-by-step explanation:

To find the number of solutions for the system of equations, we need to determine if the two equations intersect or coincide with each other. We can do this by graphing the equations or by solving them algebraically.

From the first equation, we can rewrite it as y = x² - 5x + 3. Substituting this expression for y into the second equation gives us x² - 5x + 3 = x - 6.

By simplifying and rearranging terms, we get the quadratic equation x² - 6x + 9 = 0. This quadratic equation has two solutions. Therefore, there are 2 solutions for the given system of equations.