Solve 2/(7y - 3) = 3/(y - 5) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{2}{7y-3}=\frac{3}{y-5}$$

Solve for y

$y=-\frac{1}{19}\approx -0.052631579$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to any of the values $\frac{3}{7},5$ since division by zero is not defined. Multiply both sides of the equation by $\left(y-5\right)\left(7y-3\right)$, the least common multiple of $7y-3,y-5$.

$$\left(y-5\right)\times 2=\left(7y-3\right)\times 3$$

Use the distributive property to multiply $y-5$ by $2$.

$$2y-10=\left(7y-3\right)\times 3$$

Use the distributive property to multiply $7y-3$ by $3$.

$$2y-10=21y-9$$

Subtract $21y$ from both sides.

$$2y-10-21y=-9$$

Combine $2y$ and $-21y$ to get $-19y$.

$$-19y-10=-9$$

Add $10$ to both sides.

$$-19y=-9+10$$

Add $-9$ and $10$ to get $1$.

$$-19y=1$$

Divide both sides by $-19$.

$$y=\frac{1}{-19}$$

Fraction $\frac{1}{-19}$ can be rewritten as $-\frac{1}{19}$ by extracting the negative sign.

$$y=-\frac{1}{19}$$