Determine whether the ordered pair is a solution of the inequality

(5, 12); 6y-7x.7
Is the ordered pair a solution of the inequality? no or yes
solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.
6x-y=33
6x+7y=9
What is the solution of the system of equations?

Is the system consistent or inconsistent?

Are the equations dependent or independent?

To determine whether the ordered pair (5, 12) is a solution of the inequality 6y - 7x < 7, you need to substitute the values of x and y into the inequality and check if the inequality is true or false.

1. Substitute x = 5 and y = 12 into the inequality:
6(12) - 7(5) < 7

2. Simplify:
72 - 35 < 7
37 < 7

Since 37 is NOT less than 7, the inequality is FALSE. Therefore, the ordered pair (5, 12) is NOT a solution of the inequality.

Now let's solve the system of equations using graphing:

Equation 1: 6x - y = 33
Equation 2: 6x + 7y = 9

To graph the system, follow these steps:

1. Rewrite both equations in slope-intercept form (y = mx + b):
Equation 1: y = 6x - 33
Equation 2: y = (-6/7)x + 9/7

2. Plot the points on a graph. For Equation 1, plot the y-intercept at -33 and use the slope 6/1 to get additional points. For Equation 2, plot the y-intercept at 9/7 and use the slope -6/7 to get additional points.

3. Draw lines through the points representing each equation.

After graphing, you should see that the lines intersect at a single point, indicating that there is a unique solution. This means the system is consistent.

To determine if the equations are dependent or independent, we can compare their slopes. Since the slopes are different (-6/7 vs. 6), the equations are independent.

Therefore:
- The solution of the system of equations is the point where the lines intersect.
- The system is consistent.
- The equations are independent.

To determine whether the ordered pair (5, 12) is a solution of the inequality 6y-7x<7:

1. Substitute the values of x and y from the ordered pair into the inequality.
6(12)-7(5)<7
72-35<7
37<7

2. The inequality 37<7 is not a true statement.

Therefore, the ordered pair (5, 12) is not a solution of the inequality.

Now, let's solve the system of equations by graphing and determine whether it is consistent or inconsistent, as well as whether the equations are dependent or independent.

The system of equations is:
1. 6x-y=33
2. 6x+7y=9

To solve the system by graphing:

1. Rewrite each equation in slope-intercept form (y=mx+b):
1. 6x-y=33 => y=6x-33
2. 6x+7y=9 => y=-6/7x+9/7

2. Plot the graphs of the two equations on the same coordinate plane.

Based on the graph, we can see that the two lines intersect at a single point.

The solution of the system of equations is the point where the two lines intersect, which is approximately (5, -3/7).

Since the lines intersect at a single point, the system is consistent.

Furthermore, since the two equations have different slopes, the equations are independent.

To summarize:
- The solution of the system of equations is (5, -3/7).
- The system is consistent.
- The equations are independent.

In the first question, you do not provide an inequality. 6y-7x.7 is not an inequality.

In the second question, the equations are independent. Suntract the first from the second and you get 8y = -24, so
y = -3 and 6x = 30, so x = 5.