Answer:
The two points solutions to the system of equations are: (2, 3) and (-1,6)
Step-by-step explanation:
These system of equations consists of a parabola and a line. We need to find the points at which they intersect:
[tex]x^2-2x+3=-x+5\\x^2-2x+x+3-5=0\\x^2-x-2=0\\(x-2)(x+1)=0[/tex]
Since we were able to factor out the quadratic expression, we can say that the x-values solution of the system are:
x = 2 and x = -1
Now, the associated y values we can get using either of the original equations for the system. We pick to use the linear equation for example:
when x = 2 then [tex]y=-(2)+5=3[/tex]
when x= -1 then [tex]y=-(-1)+5=6[/tex]
Then the two points solutions to the system of equations are: (2, 3) and (-1,6)
