Let's solve the given simultaneous equations using the elimination method:

Equations:

1. $2y + x = 7$
2. $y + x = 5$

Step 1: Eliminate $x$

To eliminate $x$, subtract the second equation from the first equation:

$(2y + x) - (y + x) = 7 - 5$

$2y - y + x - x = 2$

$y = 2$

Step 2: Substitute $y = 2$ into one of the original equations

Using the second equation $y + x = 5$:

$2 + x = 5$

$x = 5 - 2$

$x = 3$

Solution:

The solution to the system of equations is:

$x = 3, \, y = 2$

Would you like additional explanation on any step or to explore similar problems?

Follow-up Questions:

1. How can we verify the solution of these simultaneous equations?
2. What happens if both equations are multiplied by constants? Does elimination still work?
3. Can this problem be solved graphically? If so, how would the solution look?
4. What is the advantage of the elimination method over substitution?
5. How would this process differ if the coefficients of $x$ and $y$ were fractions?

Tip:

Always verify your solution by substituting the values of $x$ and $y$ back into