Question

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how many solutions does the system of equations below have?
$y = \frac{9}{7}x+\frac{3}{2}$
$y = \frac{-8}{3}x+\frac{7}{2}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Identify slopes of lines

The first - line has a slope $m_1=\frac{9}{7}$, and the second - line has a slope $m_2 =-\frac{8}{3}$. Since $m_1
eq m_2$, the two lines are not parallel.

Step2: Recall intersection property

Two non - parallel lines in a plane intersect at exactly one point. A system of linear equations represented by non - parallel lines has one solution.

Answer:

one solution