Questions: Solve the linear equation for (y). [5x-4y=-100] Solve the following for (y): (fracx4+fracy5=1) [y= ] Solve the equation for (h). [frac8w=frac7m+frac3h]

$Solve the linear equation for (y). [5x-4y=-100] Solve the following for (y): (fracx4+fracy5=1) [y= ] Solve the equation for (h). [frac8w=frac7m+frac3h]$

Transcript text: Solve the linear equation for $y$. \[ 5x-4y=-100 \] Solve the following for $\mathrm{y}: \frac{x}{4}+\frac{y}{5}=1$ \[ y= \] Solve the equation for $h$. \[ \frac{8}{w}=\frac{7}{m}+\frac{3}{h} \]

Solution

Solution Steps

Step 1: Solve the linear equation for $ y $ in $ 5x - 4y = -100 $

Start with the equation: \[ 5x - 4y = -100 \] Subtract $ 5x $ from both sides: \[ -4y = -100 - 5x \] Divide both sides by $ -4 $: \[ y = \frac{-100 - 5x}{-4} \] Simplify the equation: \[ y = \frac{100 + 5x}{4} \]

Step 2: Solve for $ y $ in $ \frac{x}{4} + \frac{y}{5} = 1 $

Start with the equation: \[ \frac{x}{4} + \frac{y}{5} = 1 \] Subtract $ \frac{x}{4} $ from both sides: \[ \frac{y}{5} = 1 - \frac{x}{4} \] Multiply both sides by $ 5 $: \[ y = 5 \left(1 - \frac{x}{4}\right) \] Simplify the equation: \[ y = 5 - \frac{5x}{4} \]

Step 3: Solve the equation for $ h $ in $ \frac{8}{w} = \frac{7}{m} + \frac{3}{h} $

Start with the equation: \[ \frac{8}{w} = \frac{7}{m} + \frac{3}{h} \] Subtract $ \frac{7}{m} $ from both sides: \[ \frac{8}{w} - \frac{7}{m} = \frac{3}{h} \] Take the reciprocal of both sides: \[ h = \frac{3}{\frac{8}{w} - \frac{7}{m}} \] Simplify the denominator: \[ h = \frac{3}{\frac{8m - 7w}{wm}} \] Multiply by the reciprocal: \[ h = \frac{3wm}{8m - 7w} \]