How to Solve the System of Equations: x + 2y = 6 and 2x + 4y = 10

To solve the system of equations given by x + 2y = 6 and 2x + 4y = 10, we can use either substitution or elimination method. Here, we will opt for the substitution method.

First, let’s solve the first equation for x:

x = 6 - 2y

Now, we can substitute this expression for x into the second equation:

2(6 - 2y) + 4y = 10

Expanding this gives us:

12 - 4y + 4y = 10

This simplifies to:

12 = 10

This statement is false, indicating that there are no solutions to this system of equations. In fact, the second equation can be simplified to:

x + 2y = 5

as both equations are actually representing parallel lines, thus confirming that they do not intersect. Therefore, the system of equations is inconsistent.