Question

Which of the following best describes the solution to the system of equations below?

Answer 1

Answer: OPTION A

Step-by-step explanation:

The equation of the line in slope-intercept form is:

$y=mx+b$

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

Solve for y from each equation:

$\left \{ {{5y=-4x+7} \atop {10y=-8x+14}} \right.\\\\\left \{ {{y=\frac{-4}{5}x+\frac{7}{5}} \atop {y=\frac{-8}{10}x+\frac{14}{10}}} \right.\\\\\left \{ {{y=\frac{-4}{5}x+\frac{7}{5}} \atop {y=\frac{-4}{5}x+\frac{7}{5}}} \right.$

As you can see the slope and the y-intercept of each equation are equal, this means that both are the exact same line. Therefore, you can conclude that the system has infinitely many solutions.