Question

2. How many solutions are there for the following system of equations?2 pointsy = x2 - 5x + 3y = x-6

Answer 1

Simplify the equation to obtain the value of x.

$\begin{gathered} x^2-5x+3=x-6 \\ x^2-6x+9=0 \\ x^2-3x-3x+9=0 \\ x(x-3)-3(x-3)=0 \\ (x-3)(x-3)=0 \\ x=3 \end{gathered}$

Substitute 3 for x in equation y = x - 3 to obtain the value of y.

$\begin{gathered} y=3-6 \\ =-3 \end{gathered}$

So solution of equation is (3,-3).

Thus there is one solution for system of equations.