Question

What are the ordered pairs of the

solutions for this system of equations?
f(x) = x2 – 2x + 3; f(x) = -x + 5
(2, [?]); ([ ], [])

Answer 1

The two points solutions to the system of equations are: (2, 3) and (-1,6)

Explanation:

These system of equations consists of a parabola and a line. We need to find the points at which they intersect:

`x^2-2x+3=-x+5\\x^2-2x+x+3-5=0\\x^2-x-2=0\\(x-2)(x+1)=0`

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
`y=-(2)+5=3`

when x= -1 then
`y=-(-1)+5=6`

Then the two points solutions to the system of equations are: (2, 3) and (-1,6)