Question

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how many solutions does the system of equations below have?
$y=-4x - 6$
$y=\frac{-9}{10}x+\frac{1}{3}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Identify slope of first line

The first - line equation is $y=-4x - 6$, and its slope $m_1=-4$.

Step2: Identify slope of second line

The second - line equation is $y =-\frac{9}{10}x+\frac{1}{3}$, and its slope $m_2=-\frac{9}{10}$.

Step3: Analyze relationship between slopes

Since $m_1
eq m_2$, the two lines are not parallel. Non - parallel lines in a plane intersect at exactly one point.

Answer:

one solution