185k views
0 votes
Create a system of two mixed equations in standard form where the solution is (-5,2)

User Kyle Krull
by
8.1k points

1 Answer

3 votes

Final answer:

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).

User Dharmit
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories