Q. How many solutions does the system of equations below have?y=7x−6y=7x−6Choices:(A)no solution(B)one solution(C)infinitely many solutions
Given Equations: The system of equations is given as:y=7x−6y=7x−6We need to determine how many solutions this system has.
Identical Equations: Since both equations are identical, every solution to the first equation is also a solution to the second equation.
Common Solutions: This means that any point (x,y) that lies on the line y=7x−6 will satisfy both equations simultaneously.
Infinite Solutions: Therefore, the system of equations does not have a unique solution. Instead, it has infinitely many solutions because the lines represented by the equations are the same line, and thus they intersect at all points on that line.