Question

what is the correct classification of the system of equations below?

12x - 3y = 9

y - 4x = -3

a. parallel

b. coincident

c. intersecting

Explanation:

Step1: Convert to slope - intercept form

For the first equation \(12x - 3y=9\), solve for \(y\):
Subtract \(12x\) from both sides: \(- 3y=-12x + 9\).
Divide both sides by \(-3\): \(y = 4x-3\). The slope \(m_1 = 4\).

For the second equation \(y - 4x=-3\), solve for \(y\):
Add \(4x\) to both sides: \(y=4x - 3\). The slope \(m_2 = 4\).

Step2: Analyze the equations

Since both equations have the same slope (\(m_1=m_2 = 4\)) and the same \(y\) - intercept (\(b=-3\)), the two lines are coincident (they are the same line, so they overlap completely).

Answer:

B. coincident