To solve the system of linear equations:

1. $2x + 3y = 4$
2. $y + 3x = 6$

We'll use substitution or elimination. Let's use substitution in this case.

Step 1: Solve the second equation for $y$

From $y + 3x = 6$, isolate $y$: $y = 6 - 3x$

Step 2: Substitute this expression for $y$ into the first equation

Substitute $y = 6 - 3x$ into $2x + 3y = 4$: $2x + 3(6 - 3x) = 4$ Now, simplify: $2x + 18 - 9x = 4$ $-7x + 18 = 4$ $-7x = 4 - 18$ $-7x = -14$ $x = 2$

Step 3: Substitute $x = 2$ back into the expression for $y$

Now that we know $x = 2$, substitute this into $y = 6 - 3x$: $y = 6 - 3(2)$ $y = 6 - 6$ $y = 0$

Final Solution

The solution to the system is: $x = 2, \quad y = 0$

Would you like further details or have any questions?

Here are 5 related questions:

1. How can you solve a system of equations using the elimination method?
2. What are the graphical interpretations of solutions to systems of equations?
3. How would the solution change if the system of equations was inconsistent?
4. Can you solve a 3-variable system of equations?
5. How do systems of nonlinear equations differ from linear ones?

Tip: Always check your solution by plugging the values back into both original equations.