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.
