solve the system of equations by graphing if the system is inconsistent or the equations are dependent 5x-3y=2 and 10x-6y=4
To determine whether the system of equations is consistent or the equations are dependent, let's graph the equations and see if they intersect at a single point or if they coincide.
First, let's rearrange the equations in slope-intercept form (y = mx + b):
5x - 3y = 2
-3y = -5x + 2
y = (5/3)x - (2/3)
10x - 6y = 4
-6y = -10x + 4
y = (10/6)x - (2/3)
y = (5/3)x - (2/3)
Both equations can be rewritten as y = (5/3)x - (2/3), indicating that they are the same line. They have the same slope and the same y-intercept.
Let's graph the line y = (5/3)x - (2/3):
{{{graph(400,400,-5,5,-5,5,(5/3)x-(2/3))}}}
As we can see, the two equations coincide and represent the same line. Therefore, the system of equations is dependent.
Note: If the two equations did not coincide (they were parallel and never intersected), the system would be inconsistent.