Question

How many solutions does the system have? {y=−2x+2y=x2−3x Enter your answer in the box.

Answer 1

ANSWER

The system has two solutions.

Step-by-step explanation

The given equations are


`y=-2x + 2`

and


`y={x}^(2) - 3x`

We equate both equations to obtain;


`{x}^(2) - 3x =-2x + 2`

This implies that,


`{x}^(2) - 3x +2x - 2 = 0`


`{x}^(2) - x - 2 = 0`

where a=1, b=-1,c=-2.

We find the discriminant, D=b²-4ac of this equation to be;


`D = {(-1)}^(2) - 4(1)( - 2) = 9`

Since the discriminant is greater than zero, it means the two functions intersected at two distinct points.


Hence the system has two solutions.