Linear Equations in Standard Form Coloring Page by Brittany Kiser - Free Printable

It looks like you've uploaded a worksheet titled "LINEAR EQUATIONS in Standard Form" with several problems to solve. Let's go through the task step by step.

---

🔍 Instructions on the Worksheet:

> "Solve each equation. Put your answer in standard form: \( Ax + By = C \). Then check your answer."

The standard form of a linear equation is:
\[
Ax + By = C
\]
where \( A \), \( B \), and \( C \) are integers, and \( A \geq 0 \). If \( A \) is negative, we multiply the entire equation by -1 to make it positive.

---

✔ Step-by-step Solutions:

Let’s solve each problem one by one.

---

#### 1. \( 3x + 4y = 12 \)
This is already in standard form.

✔ Answer: \( 3x + 4y = 12 \)

---

#### 2. \( 5x + 7y = 105 \)
Already in standard form.

✔ Answer: \( 5x + 7y = 105 \)

---

#### 3. \( -6x + 9y = 72 \)
We want \( A \geq 0 \), so let’s eliminate the negative coefficient of \( x \).

Divide the entire equation by the GCF of coefficients (3):

\[
-2x + 3y = 24
\]

Now, multiply both sides by -1 to make \( A \) positive:

\[
2x - 3y = -24
\]

✔ Answer: \( 2x - 3y = -24 \)

---

#### 4. \( 4x + 3y = 24 \)
Already in standard form.

✔ Answer: \( 4x + 3y = 24 \)

---

#### 5. \( -45x + 35y = 115 \)
Find GCF of 45, 35, and 115 → GCF is 5.

Divide all terms by 5:

\[
-9x + 7y = 23
\]

Make \( A \) positive by multiplying by -1:

\[
9x - 7y = -23
\]

✔ Answer: \( 9x - 7y = -23 \)

---

#### 6. \( 3x + 5y = -15 \)
Already in standard form.

✔ Answer: \( 3x + 5y = -15 \)

---

#### 7. \( 4x + 3y = -36 \)
Already in standard form.

✔ Answer: \( 4x + 3y = -36 \)

---

#### 8. \( -3x + \frac{1}{2}y = 30 \)
We need to eliminate fractions. Multiply every term by 2:

\[
-6x + y = 60
\]

Now make \( A \) positive:

Multiply by -1:

\[
6x - y = -60
\]

✔ Answer: \( 6x - y = -60 \)

---

#### 9. \( 35x - 20y = -100 \)
Find GCF of 35, 20, 100 → GCF is 5.

Divide by 5:

\[
7x - 4y = -20
\]

✔ Answer: \( 7x - 4y = -20 \)

---

#### 10. \( x + 4y = -4 \)
Already in standard form.

✔ Answer: \( x + 4y = -4 \)

---

#### 11. \( m - n = 4 \)
This is not in terms of \( x \) and \( y \), but since it's a linear equation, we can rewrite it as:

Let \( m = x \), \( n = y \), then:

\[
x - y = 4
\]

✔ Answer: \( x - y = 4 \)

---

#### 12. \( 0.75x + 7y = 105 \)
Convert decimal to fraction: \( 0.75 = \frac{3}{4} \)

So:
\[
\frac{3}{4}x + 7y = 105
\]

Multiply all terms by 4 to eliminate denominator:

\[
3x + 28y = 420
\]

✔ Answer: \( 3x + 28y = 420 \)

---

📌 Final Answers (in Standard Form):

| Problem | Answer |
|--------|--------|
| 1 | \( 3x + 4y = 12 \) |
| 2 | \( 5x + 7y = 105 \) |
| 3 | \( 2x - 3y = -24 \) |
| 4 | \( 4x + 3y = 24 \) |
| 5 | \( 9x - 7y = -23 \) |
| 6 | \( 3x + 5y = -15 \) |
| 7 | \( 4x + 3y = -36 \) |
| 8 | \( 6x - y = -60 \) |
| 9 | \( 7x - 4y = -20 \) |
| 10 | \( x + 4y = -4 \) |
| 11 | \( x - y = 4 \) |
| 12 | \( 3x + 28y = 420 \) |

---

✔ How to Check Your Answers:

For each equation, plug in values or verify that it matches the original after simplifying.

For example, for #3:
Original: \( -6x + 9y = 72 \)
After simplification: \( 2x - 3y = -24 \)

Check: Multiply \( 2x - 3y = -24 \) by 3 → \( 6x - 9y = -72 \), then multiply by -1 → \( -6x + 9y = 72 \) ✔️

All answers are consistent.

---

🧠 Tips:

- Always ensure the equation is in the form \( Ax + By = C \)
- Make sure \( A \), \( B \), and \( C \) are integers
- \( A \geq 0 \), and if possible, reduce to lowest terms

---

Let me know if you'd like this formatted for printing or if you want to graph any of these equations!