Let’s solve step by step and confirm the solution:

Step 1: Isolate $x$ in the first equation

$x + 3y = 7 \implies x = 7 - 3y$

Step 2: Substitute $x = 7 - 3y$ into the second equation

$2x + 4y = 8 \implies 2(7 - 3y) + 4y = 8$

Simplify: $14 - 6y + 4y = 8 \implies 14 - 2y = 8$

Step 3: Solve for $y$

$14 - 2y = 8 \implies -2y = -6 \implies y = 3$

Step 4: Substitute $y = 3$ into either original equation to find $x$

Using the first equation: $x + 3(3) = 7 \implies x + 9 = 7 \implies x = -2$

Step 5: Write the solution as an ordered pair

The solution is: $(x, y) = (-2, 3)$

Verification:

• First equation: $x + 3y = -2 + 3(3) = -2 + 9 = 7$ (Correct)
• Second equation: $2x + 4y = 2(-2) + 4(3) = -4 + 12 = 8$ (Correct)

The solution is consistent and valid.

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Do you want more details or have any specific questions?

Here are 5 related questions to expand your understanding:

1. How can you solve this system graphically?
2. What happens if the system of equations has no solutions or infinite solutions?
3. Can this system be solved using matrices or determinants (Cramer's Rule)?
4. How does substitution differ from elimination in solving systems of equations?
5. What real-world situations can be modeled by this system of equations?

Tip: Always verify your solution by substituting back into the original equations!