Question

solve for y
a) 8x + 4y = 2
b) 12x - 3y = 7

Explanation:

Part (a)

Step1: Isolate the term with y

Subtract \(8x\) from both sides of the equation \(8x + 4y = 2\).
\(4y = 2 - 8x\)

Step2: Solve for y

Divide both sides of the equation by 4.
\(y=\frac{2 - 8x}{4}\)
Simplify the right - hand side by dividing each term in the numerator by 4.
\(y=\frac{2}{4}-\frac{8x}{4}\)
\(y=\frac{1}{2}-2x\) or \(y=-2x + \frac{1}{2}\)

Part (b)

Step1: Isolate the term with y

Subtract \(12x\) from both sides of the equation \(12x-3y = 7\).
\(-3y=7 - 12x\)

Step2: Solve for y

Divide both sides of the equation by \(- 3\).
\(y=\frac{7 - 12x}{-3}\)
Simplify the right - hand side by dividing each term in the numerator by \(-3\).
\(y=\frac{7}{-3}-\frac{12x}{-3}\)
\(y = 4x-\frac{7}{3}\)

Answer:

a) \(y=-2x+\frac{1}{2}\)
b) \(y = 4x-\frac{7}{3}\)