Question

I’ll give branniest for the correct answer

Two skaters are practicing at the same time on the same rink. A coordinate grid is superimposed on the ice. One skater follows
the path y = - 3x + 8, while the other skater follows the curve y= - 2x^2 + 7x. Find all the points where they might collide if they
are not careful.

Answer 1

Answer: To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations:

y = -3x + 8

y = -2x^2 + 7x

We can set the two equations equal to each other and solve for x:

-3x + 8 = -2x^2 + 7x

This simplifies to:

2x^2 - 10x + 8 = 0

Dividing both sides by 2, we get:

x^2 - 5x + 4 = 0

Factoring the left side, we get:

(x - 1)(x - 4) = 0

So the solutions for x are x = 1 and x = 4.

To find the corresponding values of y, we can substitute these values of x into either equation. Let's use y = -3x + 8:

When x = 1, y = -3(1) + 8 = 5

When x = 4, y = -3(4) + 8 = -4

Therefore, the two skaters might collide at the points (1, 5) and (4, -4).

Explanation: