Question

Create a system of two mixed equations in standard form where the solution is (-5,2)

Answer 1

To create a system with the solution (-5,2), choose coefficients to create one linear equation (2x - 3y = -4) and one nonlinear equation (y = x^2 - 23) that are satisfied by the solution.

Step-by-step explanation:

To create a system of two mixed equations in standard form where the solution is (-5,2), we must find equations that have (-5,2) as their intersection point. Here are the steps to create such a system:

1. Choose arbitrary coefficients for the variables x and y and plug in the coordinates of the point to get the constant terms.
2. Make one equation linear and the other can be nonlinear, thus achieving a mixed system.

For example, we can create the system:

• 2x - 3y = -4 [Plugging in (-5,2) gives: 2(-5) - 3(2) = -4]
• x^2 + y = 23 [Plugging in (-5,2) gives: (-5)^2 + 2 = 25 + 2 = 27, which doesn't seem correct. Let's correct this equation.]

Let's try a different nonlinear equation that satisfies the point (-5,2):

• y = x^2 - 23 [Plugging in (-5,2) gives: 2 = (-5)^2 - 23 which simplifies to 2 = 25 - 23, hence, correct.]

The correct system is therefore:

• 2x - 3y = -4
• y = x^2 - 23

And this system indeed has the solution (-5,2).