Which of the following best describes the solution to the system of equations below?4x + 5y = 78x + 10y = 14A. The system of equations has infinitely many solutions. B. The system of equations has exactly one solution where x = 7/4 and y = 0 C. The system of equations has no solution. D. The system of equations has exactly one solution where x = 1 and y = 6/5

Answer: OPTION AStep-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 the y-intercept. Solve for y from each equation: [tex]\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.[/tex] 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.