Question

Write an equation with integer solutions for the system of linear equations:

x = 10, y = 0
x = 0, y = 15

A) x^2 + 2y^2 + 10 = 0
B) x^2 + 4y^2 + 100 = 0
C) x² + 2y² - 10 = 0
D) x^2 + 4y^2 - 100 = 0

Answer 1

The correct equation with integer solutions for the system of linear equations given is D) x^2 + 4y^2 - 100 = 0, as it satisfies the points (10,0) and (0,15).

Step-by-step explanation:

To find a quadratic equation with integer solutions given the system of linear equations (x = 10, y = 0) and (x = 0, y = 15), we want to create an equation that these points will satisfy. Since a quadratic equation is of the form ax2 + bx2 + c = 0, we want to find constants a, b, and c that give us the correct solutions.

We can substitute our points into the given options to determine which one provides integer solutions:

• For A) x2 + 2y2 + 10 = 0, substituting the points results in no solutions.
• For B) x2 + 4y2 + 100 = 0, substituting the points results in no solutions.
• For C) x2 + 2y2 - 10 = 0, substituting the points results in no solutions.
• For D) x2 + 4y2 - 100 = 0, substituting the points (10,0) and (0,15) results in:

• (10)2 + 4(0)2 - 100 = 100 - 100 = 0
• (0)2 + 4(15)2 - 100 = 900 - 100 = 0

Therefore, option D) x2 + 4y2 - 100 = 0 is the correct equation with integer solutions for the given system.