Question

what is the correct classification of the system of equations below?
5x + 6y = 1
y = -5x + 6
a. parallel
b. coincident
c. intersecting

Explanation:

Step1: Convert to slope - intercept form

For the equation \(5x + 6y=1\), solve for \(y\):
Subtract \(5x\) from both sides: \(6y=- 5x + 1\)
Divide by \(6\): \(y=-\frac{5}{6}x+\frac{1}{6}\)
The second equation is \(y = - 5x+6\), its slope \(m_2=-5\)
The slope of the first equation \(m_1 =-\frac{5}{6}\)

Step2: Compare slopes

Since \(m_1=-\frac{5}{6}\) and \(m_2 = - 5\), and \(m_1
eq m_2\) (so not parallel) and \(m_1\) is not a multiple of \(m_2\) in a way that would make the lines coincident (since the slopes are different and the y - intercepts \(\frac{1}{6}\) and \(6\) are also different). When two lines have different slopes, they will intersect at exactly one point.

Answer:

C. intersecting