Question

How many solutions are there to the system of equations?

Answer 1

Answer: The system of equations has NO SOLUTION.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the following system of equations:

$\left \{ {{4x-5y=5} \atop {-0.08x+0.10y=0.10}} \right.$

Write the first equation and solve for "y" in order to express it in Slope-Intercept form:

$4x-5y=5\\\\-5y=-4x+5\\\\y=\frac{-4x}{-5}+\frac{5}{-5}\\\\y=0.8x-1$

You can identify that:

$m=0.8\\b=-1$

Apply the same procedure with the second equation. Then:

$-0.08x+0.10y=0.10\\\\0.10y=0.08x+0.10\\\\y=\frac{0.08x}{0.10} +\frac{0.10}{0.10}\\\\y=0.8x+1$

You can identify that:

$m=0.8\\b=1$

The slopes of both lines are equal, therefore  the lines are parallel and the system has NO SOLUTION.

Answer 2

answer: A

(no solutions)

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