To solve the system of equations:

$2x + 2y = 16$ $x - 3y = 4$

Let's solve it step-by-step.

Step 1: Simplify the first equation

The first equation can be simplified by dividing all terms by 2: $x + y = 8$

Now we have the simplified system:

1. $x + y = 8$
2. $x - 3y = 4$

Step 2: Solve for $x$ in terms of $y$

From the first equation: $x = 8 - y$

Step 3: Substitute $x$ in the second equation

Substitute $x = 8 - y$ into the second equation: $(8 - y) - 3y = 4$

Simplify this equation: $8 - 4y = 4$ $-4y = -4$ $y = 1$

Step 4: Substitute $y = 1$ back to find $x$

Now substitute $y = 1$ into $x = 8 - y$: $x = 8 - 1$ $x = 7$

Solution

The solution to the system is: $x = 7, \quad y = 1$

Would you like a deeper breakdown of these steps or have any questions?

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Here are some related questions for further practice:

1. What are the solutions to the system $3x + 4y = 18$ and $x - 2y = 3$?
2. How would you solve a system where both equations are multiplied by constants?
3. What is the significance of parallel lines in systems of linear equations?
4. How can substitution help in solving systems with more than two equations?
5. What are the conditions for a system of linear equations to have no solution?

Tip: In systems of equations, simplifying by division first can make the calculations easier.