Simply (6x4y − 4x2y + 3xy) + (3x4y + 5x2y − 4xy).

 9x4y + 9x2y − 7xy
 9x4y − 9x2y − 7xy
 9x4y + x2y − xy
 9x4y − x2y − xy
Question 10(Multiple Choice Worth 1 points)
(05.03 MC)

Solve the system of equations using elimination.

4x + 4y = 28
3x + y = 15

 (1, 6)
 (2, 5)
 (3, 4)
 (4, 3)
Question 11(Multiple Choice Worth 1 points)
(05.05 MC)

Which of the following ordered pairs is a solution to the inequality y is greater than one fourth times x plus 5?

 (12, 8)
 (11, 7)
 (8, 6)
 (4, 7)
Question 12(Multiple Choice Worth 1 points)
(05.02, 05.03 MC)

What is the x-coordinate of the solution to the following system of equations?

x − 2y = 2
3x + y = 6

 x = −2
 x = 0
 x = 2
 x = 3
Question 13(Multiple Choice Worth 1 points)
(06.02 MC)

Simply (3ab3 − 4a2b + 6ab) − (4ab3 − 6a2b + 6ab).

 −ab3 + 2a2b
 −ab3 + 2a2b −12ab
 −ab3 − 10a2b
 −ab3 + 2a2b + 12ab

Let's work through each of these problems step by step.

### Problem 1: Simplifying the Expression
We need to simplify the expression:
\[
(6x^4y − 4x^2y + 3xy) + (3x^4y + 5x^2y − 4xy)
\]

Combine like terms:

1. Combine \(6x^4y\) and \(3x^4y\):
   \[
   6x^4y + 3x^4y = 9x^4y
   \]

2. Combine \(-4x^2y\) and \(5x^2y\):
   \[
   -4x^2y + 5x^2y = x^2y
   \]

3. Combine \(3xy\) and \(-4xy\):
   \[
   3xy - 4xy = -xy
   \]

The simplified expression is:
\[
9x^4y + x^2y − xy
\]
This corresponds to the answer **9x4y + x2y − xy**.

### Problem 2: Solving the System of Equations Using Elimination
The system of equations is:
\[
4x + 4y = 28
\]
\[
3x + y = 15
\]

First, simplify the first equation by dividing it by 4:
\[
x + y = 7 \quad \text{(Equation 1)}
\]

We already have:
\[
3x + y = 15 \quad \text{(Equation 2)}
\]

Now, subtract Equation 1 from Equation 2 to eliminate \(y\):
\[
(3x + y) - (x + y) = 15 - 7
\]
\[
2x = 8
\]
\[
x = 4
\]

Substitute \(x = 4\) back into Equation 1:
\[
4 + y = 7
\]
\[
y = 3
\]

So the solution is \((4, 3)\), corresponding to the answer **(4, 3)**.

### Problem 3: Checking Solutions to the Inequality
The inequality is:
\[
y > \frac{1}{4}x + 5
\]

Check each pair:

1. **For (12, 8)**:
   \[
   \frac{1}{4}(12) + 5 = 3 + 5 = 8 \quad (\text{Not greater, so not a solution})
   \]

2. **For (11, 7)**:
   \[
   \frac{1}{4}(11) + 5 = 2.75 + 5 = 7.75 \quad (\text{Not greater, so not a solution})
   \]

3. **For (8, 6)**:
   \[
   \frac{1}{4}(8) + 5 = 2 + 5 = 7 \quad (\text{Not greater, so not a solution})
   \]

4. **For (4, 7)**:
   \[
   \frac{1}{4}(4) + 5 = 1 + 5 = 6 \quad (7 > 6, \text{so this is a solution})
   \]

The correct answer is **(4, 7)**.

### Problem 4: Finding the x-coordinate of the System of Equations
The system of equations is:
\[
x − 2y = 2
\]
\[
3x + y = 6
\]

Let's solve by substitution or elimination. We can solve the first equation for \(x\):
\[
x = 2y + 2 \quad \text{(Equation 1)}
\]

Substitute this into the second equation:
\[
3(2y + 2) + y = 6
\]
\[
6y + 6 + y = 6
\]
\[
7y + 6 = 6
\]
\[
7y = 0
\]
\[
y = 0
\]

Substitute \(y = 0\) back into Equation 1:
\[
x = 2(0) + 2 = 2
\]

The x-coordinate is \(x = 2\), corresponding to the answer **x = 2**.

### Problem 5: Simplifying the Expression
We need to simplify:
\[
(3ab^3 − 4a^2b + 6ab) − (4ab^3 − 6a^2b + 6ab)
\]

Distribute the negative sign:
\[
3ab^3 − 4a^2b + 6ab - 4ab^3 + 6a^2b - 6ab
\]

Combine like terms:

1. Combine \(3ab^3\) and \(-4ab^3\):
   \[
   3ab^3 - 4ab^3 = -ab^3
   \]

2. Combine \(-4a^2b\) and \(6a^2b\):
   \[
   -4a^2b + 6a^2b = 2a^2b
   \]

3. Combine \(6ab\) and \(-6ab\) (they cancel out):
   \[
   6ab - 6ab = 0
   \]

The simplified expression is:
\[
-ab^3 + 2a^2b
\]
This corresponds to the answer **−ab3 + 2a2b**.

### Summary of Answers
1. **9x4y + x2y − xy**
2. **(4, 3)**
3. **(4, 7)**
4. **x = 2**
5. **−ab3 + 2a2b**

---

Do you want more details or have any questions?

Here are some related questions to expand on:

1. How would you simplify the expression \((5x^3y - 3x^2y + 2xy) + (7x^3y - 4x^2y + xy)\)?
2. What would be the solution to the system of equations \(2x + 3y = 12\) and \(4x - y = 5\)?
3. How do you solve a system of linear equations using the substitution method?
4. Which ordered pair satisfies the inequality \(y < \frac{2}{3}x + 4\)?
5. How would you solve the system of equations \(2x - 3y = 1\) and \(x + 2y = 7\) using elimination?
6. What is the y-coordinate of the solution to the system \(3x - 4y = 5\) and \(2x + y = 6\)?
7. How would you simplify the expression \((2ab^2 - 3a^2b + 4ab) - (3ab^2 - 5a^2b + 4ab)\)?
8. What happens when you add two polynomials with similar terms?

**Tip:** When simplifying expressions, always group and combine like terms to reduce the expression to its simplest form.

Explore detailed solutions for simplifying expressions and solving equations including systems of equations and inequalities. Learn step-by-step methods for simplifying algebraic expressions and solving systems of linear equations.

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