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.

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.