Question

Select the correct answer.

How many real solutions exist for this system of equations?

y = -x + 1

y = -x2 + 4x − 2

A.
zero
B.
one
C.
two
D.
infinite

Answer 1

Two

Explanation:

I got it right, see image

Answer 2

Option C. The given system has two solutions.

Solution:

The given equations are,

`y = -x + 1`

`y = -x^2 + 4x-2`

From the equation we can say,

`-x+1 = -x^2+ 4x-2`

`\Rightarrow-x^(2)+4 x-2+x-1=0`

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

We know that the quadratic formula to solve this,

x has two values which are
`\frac{(-b+\sqrt{b^(2)-4 a c})}{2 a} \ and \ \frac{(-b-\sqrt{\left.b^(2)-4 a c\right)}}{2 a}`

Here, a = (-1), b = 5 , c = -3

So,
`x=\frac{(-5+\sqrt{(5)^(2)-4 x(-1)} *(-3))}{2 *(-1)}=((-5+√(25-12)))/(-2)=((-5+√(13)))/(-2)=((5-√(13)))/(2)`

Again
`x=((5+√(13)))/(2)`

Hence, x has two solutions.