Question

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how many solutions does the system of equations below have?
$y = \frac{9}{10}x + 2$
$y = \frac{-2}{9}x + \frac{2}{3}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Compare the slopes

The first - equation is $y=\frac{9}{10}x + 2$ with slope $m_1=\frac{9}{10}$. The second - equation is $y=\frac{-2}{9}x+\frac{2}{3}$ with slope $m_2 =-\frac{2}{9}$. Since $m_1
eq m_2$.

Step2: Determine the number of solutions

Two non - parallel lines (lines with different slopes) in a plane intersect at exactly one point. So the system of equations has one solution.

Answer:

one solution