$$\left. \begin{array} { l } { \frac { 2 - y } { y + 7 } = \frac { 3 } { 5 } } \end{array} \right.$$
Solve for y
$y = -\frac{11}{8} = -1\frac{3}{8} = -1.375$
Steps for Solving Linear Equation
Variable $y$ cannot be equal to $-7$ since division by zero is not defined. Multiply both sides of the equation by $5\left(y+7\right)$, the least common multiple of $y+7,5$.
$$5\left(2-y\right)=3\left(y+7\right)$$
Use the distributive property to multiply $5$ by $2-y$.
$$10-5y=3\left(y+7\right)$$
Use the distributive property to multiply $3$ by $y+7$.
$$10-5y=3y+21$$
Subtract $3y$ from both sides.
$$10-5y-3y=21$$
Combine $-5y$ and $-3y$ to get $-8y$.
$$10-8y=21$$
Subtract $10$ from both sides.
$$-8y=21-10$$
Subtract $10$ from $21$ to get $11$.
$$-8y=11$$
Divide both sides by $-8$.
$$y=\frac{11}{-8}$$
Fraction $\frac{11}{-8}$ can be rewritten as $-\frac{11}{8}$ by extracting the negative sign.
