Certainly! Let's solve each problem step by step.
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:
\(y = 2\)
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:
\(y = 7\)
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:
\(y = -\frac{2}{3}\)
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:
\(y = 8\)
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:
\(y = -1\)
Problem 7
Equation:
\(-x = 8 - 4y\)
Step 1: Rearrange to isolate \(y\).
\[4y = 8 + x\]
\[y = \frac{1}{4}x + 2\]
Final Answer:
\(y = \frac{1}{4}x + 2\)
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:
\(y = 1\)
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:
\(y = 12\)
Summary of Answers:
- \(y = 2\)
- \(y = 7\)
- \(y = -\frac{2}{3}\)
- \(y = 8\)
- \(y = -1\)
- \(y = \frac{1}{4}x + 2\)
- \(y = 1\)
- \(y = 12\)