Question

It is possible to get 2 solutions when the system of equations is: (check all that apply)

Answer 1

Answer:

A system of the equation of a circle and a linear equation

A system of the equation of a parabola and a linear equation

Step-by-step explanation:

Let us verify our answer

A system of the equation of a circle and a linear equation

Let an equation of a circle as $x^2+ y^2 = 1$ ..........(1)

Let a liner equation Y = x ............(2)

substitute (2) in (1)

$x^2 + x^2 = 1\\2x^2 = 1$

$x^2 = \frac{1}{\sqrt{2} } \\x = +\frac{1}{\sqrt{2} } , -\frac{1}{\sqrt{2} }$  so Y = $+\frac{1}{\sqrt{2} } , -\frac{1}{\sqrt{2} }$

so the two solution are ( $(\frac{1}{\sqrt{2} } ,\frac{1}{\sqrt{2} }) (-\frac{1}{\sqrt{2} }, -\frac{1}{\sqrt{2} }$)

A system of the equation of a parabola and a linear equation

Let equation of Parabola be $y^2 = x$

and linear equation y = x

substitute

$x^2 = x\\x^2 - x= 0\\x(x-1) = \\x = 0 , 1$

Y = 0,1

so the two solutions will be (0,0) and (1,1)