Question

solve for the value of y.

Explanation:

Step1: Set up the equation

Since the two angles are supplementary (they form a linear pair), their sum is \(180^{\circ}\). So, \(8y+(6y - 2)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(8y+6y-2=(8 + 6)y-2=14y-2\). The equation becomes \(14y-2 = 180\).

Step3: Isolate the term with \(y\)

Add \(2\) to both sides of the equation: \(14y-2+2=180 + 2\), which simplifies to \(14y=182\).

Step4: Solve for \(y\)

Divide both sides by \(14\): \(y=\frac{182}{14}\).

Answer:

\(y = 13\)