Question

Write the system of equations for the following scenario: The sum of twice the square of the first number plus the second number is 9. The difference between twice the first number and the second number is 15.

Linear Equation: _______
Quadratic Equation:______

Answer 1

The system of equations is:

Linear Equation: 2x^2 + y = 9

Quadratic Equation: 2x - y = 15

Step-by-step explanation:

Define variables:

Let x represent the first number and y represent the second number.

Translate the first sentence into an equation:

"The sum of twice the square of the first number plus the second number is 9" can be written as:

2x^2 + y = 9

Translate the second sentence into an equation:

"The difference between twice the first number and the second number is 15" can be written as:

2x - y = 15

Therefore, the system of equations is:

Linear Equation: 2x^2 + y = 9

Quadratic Equation: 2x - y = 15