describe the system 6x minus 2y equals 10 and 9x minus 3y equals 8 as consistent and independent, consistent and dependent , or inconsistent. explain. i put consistent and dependent .

If 6x - 2y = 10, then (if you multiply both sides by 3/2) you can show that 9x - 3y must equal 15. That is inconsistent with your second equation.

To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to analyze the slopes of the lines formed by the equations.

The given system of equations is:
1) 6x - 2y = 10
2) 9x - 3y = 8

To find the slopes of the lines, we will rewrite the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

1) 6x - 2y = 10
Rearrange the equation to isolate y:
-2y = -6x + 10
Divide both sides by -2:
y = 3x - 5

So, the slope of the first equation is 3.

2) 9x - 3y = 8
Rearrange the equation to isolate y:
-3y = -9x + 8
Divide both sides by -3:
y = 3x - 8/3

So, the slope of the second equation is also 3.

Since both equations have the same slope, 3, the lines represented by the equations are parallel.

Now, we need to consider the y-intercepts. The y-intercept of the first equation (equation 1) is -5, while the y-intercept of the second equation (equation 2) is -8/3.

Since the lines are parallel and have different y-intercepts, the system of equations is inconsistent. This means there are no solutions that satisfy both equations simultaneously, and the graph of the equations does not intersect.