How many ordered pairs satisfy the system of equations shown?y = x2-3x-10y=(x+2)(x-5)

The system of equations given is:

y = x^2 - 3x - 10 y = (x + 2)(x - 5)

To find the ordered pairs that satisfy the system, we need to solve the system of equations. Here are the steps:

Step 1: Set the two equations equal to each other since they both equal y:

x^2 - 3x - 10 = (x + 2)(x - 5)

Step 2: Simplify the right side of the equation:

x^2 - 3x - 10 = x^2 - 3x - 10

Step 3: Subtract x^2, add 3x, and add 10 from both sides to get:

0 = 0

This means that the two equations are identical, and any (x, y) that satisfies one equation will satisfy the other.

The solutions to the equation y = x^2 - 3x - 10 can be found by setting y = 0 and solving for x:

x^2 - 3x - 10 = 0

This can be factored to:

(x - 5)(x + 2) = 0

Setting each factor equal to zero gives the solutions x = 5 and x = -2.

Substituting x = 5 into the equation y = x^2 - 3x - 10 gives y = 0. Substituting x = -2 gives y = 0.

So, the ordered pairs that satisfy the system of equations are (5, 0) and (-2, 0).