Question

find the value of y.
6y
2
4y+5
3
© algebra einstein, 2023

Explanation:

Step1: Apply the property of parallel lines and transversals (Proportionality)

When three or more parallel lines are cut by transversals, the segments are proportional. So, we have the proportion \(\frac{6y}{2}=\frac{4y + 5}{3}\).

Step2: Cross - multiply

Cross - multiplying gives \(6y\times3=2\times(4y + 5)\).

$$18y=8y + 10$$

Step3: Solve for \(y\)

Subtract \(8y\) from both sides: \(18y-8y=8y + 10-8y\), which simplifies to \(10y=10\).
Divide both sides by \(10\): \(y=\frac{10}{10}\).

Answer:

\(y = 1\)