Question

6 from unit 2, lesson 17 elena is solving this system of equations: $\begin{cases}10x - 6y = 16\\5x - 3y = 8end{cases}$ she multiplies the second equation by 2, then subtracts the resulting equation from the first. to her surprise, she gets the equation 0 = 0. what is special about this system of equations? why does she get this result, and what does it mean about the solutions? (if you are not sure, try graphing them.) unit 4, lesson 1

Explanation:

Step1: Multiply second equation

Multiply $5x - 3y=8$ by 2, we get $10x - 6y = 16$.

Step2: Analyze subtraction result

Subtracting $10x - 6y = 16$ from $10x - 6y = 16$ gives $0 = 0$. This means the two equations are equivalent. Geometrically, they represent the same line. So, any point on the line is a solution, resulting in infinitely many solutions.

Answer:

The system of equations has infinitely many solutions.