Question

StartLayout Enlarged left-brace 1st row x² + y² = 25 2nd row 2x + y = 25 EndLayout 0, –5) and (–5, 5) (0, –5) and (5, –15) (0, –5) and (–4, 3) (0, –5) and (4, –13)

Answer 1

Answer:

C. (0,-5) (-4,3)

Step-by-step explanation:

Answer 2

Answer:

The line does not intersect the curve

Step-by-step explanation:

Assuming that we are looking for the points of intersection of

${x}^{2} + {y}^{2} = 25$

and

$2x + y = 25$

We make y the subject in the second equation to get:

$y = 25 - 2x$

When we substitute into the first equation:

${x}^{2} + {(25 -2 x)}^{2} = 25$

Let us expand to get:

${x}^{2} + 625 - 100x + 4 {x}^{2} = 25$

We obtain the standard form

$5 {x}^{2} - 100x + 600 = 0$

Divide through by 5

${x}^{2} - 20x + 120 = 0$

The discriminant is

${( - 20)}^{2} - 4 \times 1 \times 120 = - 80$

Hence the quadratic equation has no real roots.

This means the line and point has no point of intersection.