To find the point of intersection for the pair of lines:

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

We can solve this system of linear equations either by substitution or elimination. Let's use elimination:

Step 1: Add the two equations.

We can add the two equations to eliminate $y$:

$(x + 2y) + (3x - 2y) = 4 + 4$

Simplifying:

$x + 3x + 2y - 2y = 8$

$4x = 8$

Step 2: Solve for $x$.

Divide both sides by 4:

$x = \frac{8}{4} = 2$

Step 3: Substitute $x = 2$ back into one of the original equations to solve for $y$.

We'll use the first equation $x + 2y = 4$:

$2 + 2y = 4$

Now subtract 2 from both sides:

$2y = 2$

Divide by 2:

$y = 1$

Final Answer:

The point of intersection is $(2, 1)$.

Let me know if you need more details or further clarification.

Here are some related questions:

1. How do you solve systems of equations using substitution?
2. What happens if the lines are parallel? How can we recognize this?
3. How does graphing help in finding the intersection of lines?
4. What is the general solution to a system of two linear equations?
5. How would this process change if the coefficients were fractions?

Tip: When solving a system of equations, always check your solution by plugging the values back into both original equations.