To determine whether specific values are solutions to a linear equation, systematically substitute each value for the variable and simplify both sides.

For example, test two values for the equation $5y+3=10y-4$:

Testing $y=\frac{3}{5}$:

1. Substitute: $5\left(\frac{3}{5}\right) + 3 = 10\left(\frac{3}{5}\right) - 4$
2. Multiply: $3 + 3 = 6 - 4$
3. Simplify: $6 = 2$. Since this statement is false, $y=\frac{3}{5}$ is not a solution.

Testing $y=\frac{7}{5}$:

1. Substitute: $5\left(\frac{7}{5}\right) + 3 = 10\left(\frac{7}{5}\right) - 4$
2. Multiply: $7 + 3 = 14 - 4$
3. Simplify: $10 = 10$. Since this statement is true, $y=\frac{7}{5}$ is a solution.