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?

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.