Question

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how many solutions does the system of equations below have?

$y = 9x - 6$
$y = 9x - 6$

no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze the system

The two equations $y = 9x - 6$ and $y = 9x - 6$ are identical.

Step2: Recall solution - type rule

For a system of linear equations $a_1x + b_1y=c_1$ and $a_2x + b_2y=c_2$, when $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, there are infinitely many solutions. Here, $a_1 = - 9,b_1 = 1,c_1=6,a_2=-9,b_2 = 1,c_2 = 6$, and $\frac{-9}{-9}=\frac{1}{1}=\frac{6}{6}=1$.

Answer:

Infinitely many solutions