You have a system of linear equations:

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

We can solve this system using either substitution or elimination. Let's use substitution for this example.

Step 1: Solve one equation for one variable

From equation (1):
$2x + y = 6$
Solve for $y$:
$y = 6 - 2x$

Step 2: Substitute into the second equation

Substitute $y = 6 - 2x$ into equation (2):
$3x + 4y = 4$
$3x + 4(6 - 2x) = 4$

Step 3: Simplify and solve for $x$

Distribute the 4:
$3x + 24 - 8x = 4$
Combine like terms:
$-5x + 24 = 4$
Subtract 24 from both sides:
$-5x = 4 - 24$
$-5x = -20$

Now, divide by -5:
$x = 4$

Step 4: Solve for $y$

Substitute $x = 4$ into $y = 6 - 2x$:
$y = 6 - 2(4)$
$y = 6 - 8$
$y = -2$

Solution:

The solution to the system is:
$x = 4$ and $y = -2$

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Would you like further details or clarification on any steps? Here are some related questions to explore:

1. What would happen if we solved the system using elimination instead of substitution?
2. How would we solve this system if both equations had fractions?
3. How can you check that the solution $(4, -2)$ is correct by substitution?
4. What would happen if there was no solution or infinite solutions in this system?
5. How do you interpret the graphical representation of this system of equations?

Tip: When solving a system of equations, both substitution and elimination are powerful methods—try both to become comfortable with choosing the one that suits the problem best.