Question

what is the correct classification of the system of equations below?
14x + 2y = 10
y + 7x = -5
a. parallel
b. coincident
c. intersecting

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(14x + 2y=10\), solve for \(y\):
Subtract \(14x\) from both sides: \(2y=- 14x + 10\)
Divide by 2: \(y=-7x + 5\)
The slope \(m_1=-7\) and the y - intercept \(b_1 = 5\).

For the second equation \(y + 7x=-5\), solve for \(y\):
Subtract \(7x\) from both sides: \(y=-7x-5\)
The slope \(m_2=-7\) and the y - intercept \(b_2=-5\).

Step2: Analyze slopes and y - intercepts

We see that the slopes of the two lines are equal (\(m_1 = m_2=-7\)) but the y - intercepts are different (\(b_1 = 5\) and \(b_2=-5\)).
When two lines have the same slope but different y - intercepts, they are parallel lines.

Answer:

A. parallel