Question

Which system of equations does this graph represent?

Linear graph and parabola.
They intersect at negative 1, 3 and 2, 6
a.y = x2 − 5 y = −x − 3
b.y = x2 + 2 y = x + 4
c.y = x2 + 3 y = −x + 2
d.y = x2 + 4 y = −x − 1

Answer 1

i'm going to guess ur answer will be B

Answer 2

The correct options is b.

Explanation:

It is given that the line and graph intersects each other at (-1,3) and (2,6).

The points (-1,3) and (2,6) must be lie on the line and parabola. It is possible if the points satisfies the equation of line and parabola.

In option a, the equation of line is

`y=-x-3`

Put (-1,3)

`3=-(-1)-3`

`3=-2`

This statement is not true, therefore the point (-1,3) does not lines on the line. Option a is incorrect.

Similarly, in option c and d the points does not satisfy the equation of lines. So, options c and d are incorrect.

In options b, the given equations are

`y=x^2+2` ... (1)

`y=x+4` .... (2)

Equate both equations,

`x^2+2=x+4`

`x^2-x-2=0`

`x^2-2x+x-2=0`

`(x+1)(x+2)=0`

`x=-1,2`

Put these values in equation 2.

`y=-1+4=3`

`y=2+4=6`

Therefore the intersection point of equation (1) and (2) are (-1,3) and (2,6). Option b is correct.