To solve the system by substitution, we have the following equations:

1. $y = 3x + 28$
2. $y = -4x$

Since both equations equal $y$, we can set them equal to each other:

$3x + 28 = -4x$

Step 1: Solve for $x$

Combine like terms by adding $4x$ to both sides:

$3x + 4x + 28 = 0$

$7x + 28 = 0$

Now, subtract 28 from both sides:

$7x = -28$

Then, divide by 7:

$x = -4$

Step 2: Substitute $x = -4$ into one of the original equations to find $y$

Let's substitute into the first equation:

$y = 3(-4) + 28$

$y = -12 + 28$

$y = 16$

Solution

The solution to the system is:

$(x, y) = (-4, 16)$

Would you like further details, or do you have any questions?

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Here are some related questions for practice:

1. How would the solution change if the second equation were $y = -4x + 10$?
2. What is the geometric interpretation of solving a system of equations like this one?
3. How would you solve the system if it were given in standard form?
4. Can you explain how to check if the solution to the system is correct?
5. How does substitution compare to the elimination method for solving systems?

Tip: When solving by substitution, always isolate one variable first to simplify the substitution step.