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Anna71 [15]
3 years ago
15

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

Mathematics
1 answer:
navik [9.2K]3 years ago
3 0
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.
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