Question

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

Answer 1

By solving given equation and then finding discriminant we get that this system of equations have 2 solutions

What is system of equations?

Collection of two or more equations with a same set of unknowns is called system of equations.

Given equation

$y=-2 x+2\ \ ...(1)\\\\y=x^{2}-3 x \ \ \ ...(2)$

From equation (1) and (2)

$x^{2}-3 x=-2 x+2\\\\x^{2}-3 x+2 x-2=0\\\\x^{2}-x-2=0$

This is a quadratic equation

So discriminant

$D=b^2-4ac$

$D=(-1)^2-4(1)(-2)\\D=1+8\\D=9$

As D is >0 so we will get two values of x

and two values of y corresponding to values of x

By solving given equation and then finding discriminant we get that this system of equations have 2 solutions

To know more about quadratic equations visit: https://brainly.com/question/2263981