Question

1. $1 - y = -x$\
2. $2 - 3y = -2x$\
3. $\frac{1}{4}y = -1 + \frac{5}{8}x$\
4. $0 = 1 - \frac{7}{20}x + \frac{1}{5}y$

Explanation:

Let's solve each equation one by one.

Equation 7: \(1 - y = -x\)

Step 1: Rearrange to slope - intercept form (\(y=mx + b\))

We want to solve for \(y\). Add \(y\) to both sides and add \(x\) to both sides:
\(x + 1=y\) or \(y=x + 1\)

Equation 9: \(2-3y=-2x\)

Step 1: Isolate the term with \(y\)

Subtract 2 from both sides: \(-3y=-2x - 2\)

Step 2: Solve for \(y\)

Divide both sides by \(- 3\): \(y=\frac{-2x-2}{-3}=\frac{2x + 2}{3}=\frac{2}{3}x+\frac{2}{3}\)

Equation 8: \(\frac{1}{4}y=-1+\frac{5}{8}x\)

Step 1: Solve for \(y\)

Multiply both sides by 4 to eliminate the fraction:
\(y = 4\times(-1)+4\times\frac{5}{8}x=-4+\frac{20}{8}x=-4+\frac{5}{2}x\)
We can also write it as \(y=\frac{5}{2}x - 4\)

Equation 10: \(0 = 1-\frac{7}{20}x+\frac{1}{5}y\)

Step 1: Isolate the term with \(y\)

Subtract 1 and add \(\frac{7}{20}x\) to both sides: \(\frac{1}{5}y=\frac{7}{20}x - 1\)

Step 2: Solve for \(y\)

Multiply both sides by 5: \(y = 5\times\frac{7}{20}x-5\times1=\frac{7}{4}x - 5\)

Final Answers:

• Equation 7: \(y=x + 1\)
• Equation 9: \(y=\frac{2}{3}x+\frac{2}{3}\)
• Equation 8: \(y=\frac{5}{2}x - 4\)
• Equation 10: \(y=\frac{7}{4}x - 5\)

Answer:

Let's solve each equation one by one.

Equation 7: \(1 - y = -x\)

Step 1: Rearrange to slope - intercept form (\(y=mx + b\))

We want to solve for \(y\). Add \(y\) to both sides and add \(x\) to both sides:
\(x + 1=y\) or \(y=x + 1\)

Equation 9: \(2-3y=-2x\)

Step 1: Isolate the term with \(y\)

Subtract 2 from both sides: \(-3y=-2x - 2\)

Step 2: Solve for \(y\)

Divide both sides by \(- 3\): \(y=\frac{-2x-2}{-3}=\frac{2x + 2}{3}=\frac{2}{3}x+\frac{2}{3}\)

Equation 8: \(\frac{1}{4}y=-1+\frac{5}{8}x\)

Step 1: Solve for \(y\)

Multiply both sides by 4 to eliminate the fraction:
\(y = 4\times(-1)+4\times\frac{5}{8}x=-4+\frac{20}{8}x=-4+\frac{5}{2}x\)
We can also write it as \(y=\frac{5}{2}x - 4\)

Equation 10: \(0 = 1-\frac{7}{20}x+\frac{1}{5}y\)

Step 1: Isolate the term with \(y\)

Subtract 1 and add \(\frac{7}{20}x\) to both sides: \(\frac{1}{5}y=\frac{7}{20}x - 1\)

Step 2: Solve for \(y\)

Multiply both sides by 5: \(y = 5\times\frac{7}{20}x-5\times1=\frac{7}{4}x - 5\)

Final Answers:

• Equation 7: \(y=x + 1\)
• Equation 9: \(y=\frac{2}{3}x+\frac{2}{3}\)
• Equation 8: \(y=\frac{5}{2}x - 4\)
• Equation 10: \(y=\frac{7}{4}x - 5\)