5x-3y=2 and 10x-6y=4 solve the system of equations by graphing if the system is inconsistent or the equations are dependent
To solve the system of equations by graphing, we can rearrange both equations to solve for y:
Equation 1: 5x - 3y = 2
-3y = 2 - 5x
y = (5/3)x - 2/3
Equation 2: 10x - 6y = 4
-6y = 4 - 10x
y = (10/6)x - 2/3
Simplifying, we get y = (5/3)x - 2/3
These two equations have the same slope and y-intercept, which means they are dependent.
When graphed, these two equations will produce the same line and will intersect at infinitely many points.
Hence, the system of equations is dependent.