Question

Solve problems 2-9 please and show all your work.

2))) -4+xy= -2y ; X=0
Gather the Y’s
Answer: y=4/x+2 ; y=2

3))) 5/6y=x-25/6 ; X=10
Answer: y=6/5x-5; y=7

4))) 16=-5x-9y; X=-2
Answer: y=-5/9x - 16/9 ; y=-2/3

5))) 1/4y= -1- 3/8x ; X=-8
Answer: y=-3/2x -4 ; y=8

6))) 2y= -3xy-5 ; X=1
Gather the Y’s
Answer: y=-5/3x+2 ; y=-1

7))) -X=8-4y
Answer : y=1/4x+2

8))) -2x=7y-13; X=3
Answer: y=-2/7x+13/7; y=1

9))) 5xy = -7y+24 ; X=-1
Gather the Y’s
Answer: y=24/5x+7 ; y=12

Answer 1

Certainly! Let's solve each problem step by step.

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### Problem 2
**Equation:**
\(-4 + xy = -2y\)
**Given:** \(x = 0\)

**Step 1: Substitute \(x = 0\) into the equation.**
\(-4 + 0 \cdot y = -2y\)
This simplifies to:
\(-4 = -2y\)

**Step 2: Solve for \(y\).**
Dividing both sides by -2:
\[y = \frac{-4}{-2} = 2\]

**Final Answer:**
\(y = 2\)

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### Problem 3
**Equation:**
\(\frac{5}{6}y = x - \frac{25}{6}\)
**Given:** \(x = 10\)

**Step 1: Substitute \(x = 10\) into the equation.**
\(\frac{5}{6}y = 10 - \frac{25}{6}\)

**Step 2: Simplify the right side.**
Convert 10 into sixths:
\[10 = \frac{60}{6}\]
Now:
\[\frac{5}{6}y = \frac{60}{6} - \frac{25}{6} = \frac{35}{6}\]

**Step 3: Solve for \(y\).**
Multiply both sides by \(\frac{6}{5}\):
\[y = \frac{6}{5} \cdot \frac{35}{6} = \frac{35}{5} = 7\]

**Final Answer:**
\(y = 7\)

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### Problem 4
**Equation:**
\(16 = -5x - 9y\)
**Given:** \(x = -2\)

**Step 1: Substitute \(x = -2\) into the equation.**
\(16 = -5(-2) - 9y\)

**Step 2: Simplify.**
\(16 = 10 - 9y\)
Now, isolate \(y\):
\(-9y = 16 - 10\)
\(-9y = 6\)

**Step 3: Solve for \(y\).**
\[y = \frac{-6}{9} = -\frac{2}{3}\]

**Final Answer:**
\(y = -\frac{2}{3}\)

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### Problem 5
**Equation:**
\(\frac{1}{4}y = -1 - \frac{3}{8}x\)
**Given:** \(x = -8\)

**Step 1: Substitute \(x = -8\) into the equation.**
\(\frac{1}{4}y = -1 - \frac{3}{8}(-8)\)

**Step 2: Simplify the right side.**
\(-\frac{3}{8}(-8) = 3\):
Now:
\(\frac{1}{4}y = -1 + 3\)
\(\frac{1}{4}y = 2\)

**Step 3: Solve for \(y\).**
Multiplying both sides by 4:
\[y = 8\]

**Final Answer:**
\(y = 8\)

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### Problem 6
**Equation:**
\(2y = -3xy - 5\)
**Given:** \(x = 1\)

**Step 1: Substitute \(x = 1\) into the equation.**
\(2y = -3(1)y - 5\)
This simplifies to:
\(2y = -3y - 5\)

**Step 2: Gather the \(y\) terms.**
Adding \(3y\) to both sides:
\(2y + 3y = -5\)
\(5y = -5\)

**Step 3: Solve for \(y\).**
\[y = \frac{-5}{5} = -1\]

**Final Answer:**
\(y = -1\)

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### Problem 7
**Equation:**
\(-x = 8 - 4y\)

**Step 1: Rearrange to isolate \(y\).**
\[4y = 8 + x\]
\[y = \frac{1}{4}x + 2\]

**Final Answer:**
\(y = \frac{1}{4}x + 2\)

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### Problem 8
**Equation:**
\(-2x = 7y - 13\)
**Given:** \(x = 3\)

**Step 1: Substitute \(x = 3\) into the equation.**
\(-2(3) = 7y - 13\)
\(-6 = 7y - 13\)

**Step 2: Solve for \(y\).**
Adding 13 to both sides:
\(7y = 7\)
So,
\[y = 1\]

**Final Answer:**
\(y = 1\)

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### Problem 9
**Equation:**
\(5xy = -7y + 24\)
**Given:** \(x = -1\)

**Step 1: Substitute \(x = -1\) into the equation.**
\(5(-1)y = -7y + 24\)
Simplifying:
\(-5y = -7y + 24\)

**Step 2: Gather the \(y\) terms.**
Adding \(7y\) to both sides:
\(-5y + 7y = 24\)
\(2y = 24\)

**Step 3: Solve for \(y\).**
\[y = \frac{24}{2} = 12\]

**Final Answer:**
\(y = 12\)

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### Summary of Answers:
2. \(y = 2\)
3. \(y = 7\)
4. \(y = -\frac{2}{3}\)
5. \(y = 8\)
6. \(y = -1\)
7. \(y = \frac{1}{4}x + 2\)
8. \(y = 1\)
9. \(y = 12\)