Addressing the Linear Duo: Solve the System with 5x-y=0 and 10x-2y=0

To solve this system of equations, we'll determine if the equations are equivalent, which would imply infinite solutions.

First, observe the two equations:

• Equation 1: $5x - y = 0$
• Equation 2: $10x - 2y = 0$

Now, let's simplify Equation 2 by dividing every term by 2:

$\frac{10x}{2} - \frac{2y}{2} = \frac{0}{2}$

This simplifies to:

$5x - y = 0$

We see that simplifying the second equation results in the first equation:

Both equations are indeed the same, $5x - y = 0$.

Therefore, these two equations represent the same line in a coordinate plane, meaning they have an infinite number of solutions along this line.

There are infinite solutions.