Questions: 6-(2y-5x)/2=7x+1 and 18x-4y=9

6-(2y-5x)/2=7x+1 and 18x-4y=9
Transcript text: $6-\frac{2 y-5 x}{2}=7 x+1$ and $18 x-4 y=9$
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Solution

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Solution Steps

To express the first equation in slope-intercept form, we need to isolate \( y \) on one side of the equation. The slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Solution Approach
  1. Start with the given equation: \( 6 - \frac{2y - 5x}{2} = 7x + 1 \).
  2. Multiply both sides by 2 to eliminate the fraction.
  3. Rearrange the equation to isolate \( y \) on one side.
Step 1: Start with the Given Equation

We start with the given equation: \[ 6 - \frac{2y - 5x}{2} = 7x + 1 \]

Step 2: Eliminate the Fraction

Multiply both sides by 2 to eliminate the fraction: \[ 2 \left( 6 - \frac{2y - 5x}{2} \right) = 2 \left( 7x + 1 \right) \] This simplifies to: \[ 12 - (2y - 5x) = 14x + 2 \]

Step 3: Simplify the Equation

Simplify the equation by distributing and combining like terms: \[ 12 - 2y + 5x = 14x + 2 \]

Step 4: Isolate \( y \)

Rearrange the equation to isolate \( y \): \[ 12 + 5x - 14x - 2 = 2y \] \[ 10 - 9x = 2y \]

Step 5: Solve for \( y \)

Divide both sides by 2 to solve for \( y \): \[ y = \frac{10 - 9x}{2} \] \[ y = 5 - \frac{9x}{2} \]

Final Answer

\(\boxed{y = 5 - \frac{9x}{2}}\)

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