StartLayout Enlarged left-brace 1st row negative 10 x squared minus 10 y squared = negative 300 2nd row 5 x squared + 5 y squared = 150 EndLayout Which statement describes why the system has infinite solutions?

Answer: The two system of equations has infinite number of solution because both equations are the same and can be represented by just one equation with 2 variables. When there is only a presence of one equation with 2 variables, the equation will produce infinite number of solutions.

Step-by-step explanation:

Given the simultaneous equation,

-10x² - 10y² = - 300 ... (1)

5x² + 5y² = 150

Dividing equation 1 by - 10 and equation 2 by 5 we have;

x² + y² = 30 ... (3)

x² + y² = 30 ... (4)

Adding both equations 3 and 4we have;

2x² + 2y² = 60

x² + y² = 30 ... (5)

As you can clearly see that addition of both equation 3 and 4 gave us back one of the equations we added (equation 5). This scenario shows that the x and y variable cannot have a single solution but infinite number of solution.

Condition for a system of equation to have infinite number of solution is when after reducing the simultaneous equation, we generate just one equation with 2 variables.