Answer: The system of equations has NO SOLUTION.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the following system of equations:
[tex]\left \{ {{4x-5y=5} \atop {-0.08x+0.10y=0.10}} \right.[/tex]
Write the first equation and solve for "y" in order to express it in Slope-Intercept form:
[tex]4x-5y=5\\\\-5y=-4x+5\\\\y=\frac{-4x}{-5}+\frac{5}{-5}\\\\y=0.8x-1[/tex]
You can identify that:
[tex]m=0.8\\b=-1[/tex]
Apply the same procedure with the second equation. Then:
[tex]-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[/tex]
You can identify that:
[tex]m=0.8\\b=1[/tex]
The slopes of both lines are equal, therefore the lines are parallel and the system has NO SOLUTION.
