SOLUTION: Solve the system of equations by graphing. Then classify the system. 2x + y = -3 3x + 4y = -27 What is the solution of the system?? Is the system consistant or inco

Question 328106: Solve the system of equations by graphing. Then classify the system.

2x + y = -3
3x + 4y = -27

What is the solution of the system??
Is the system consistant or inconsistant?
Are the equations dependant or independant??
Could you also please show me what the graph looks like?
Found 2 solutions by solver91311, Fombitz:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Start with either one of your equations.

Step 1. Pick a value for x. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier.

Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results.

Step 3. Take the value of x that you selected for step 1 and the value of y that you calculated in step 2 and form an ordered pair (x,y).

Step 4. Plot the ordered pair from Step 3 on your graph. Remember that the x value is the distance right or left along the horizontal axis and the y value is the distance up or down along the vertical axis.

Step 5. Repeat steps 1 through 4 with a different value for x.

Step 6. Draw a line across your graph that passes through the two points that you plotted.

Step 7. Repeat steps 1 through 6 using the other equation.

The point where the lines intersect is the solution, because the coordinates of that point will satisfy (read: make true) both of your equations. You need to determine, by inspection of the graph, what the coordinates of that point are and report your answer as an ordered pair, (x,y), using those coordinates. To check your answer, you should substitute this set of coordinates into each of your original equations and verify that you have a true statement for each of the equations.

If there is at least one ordered pair in the solution set, then the system is consistent. If not, the system is inconsistent.

If there is exactly one ordered pair in the solution set, then the system is independent. If the solution set has infinite elements, then the system is dependent.

I'll send you a picture of the graph after you describe your solution set.

John

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

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Looks like (3,-9) is a solution.
Verify using the equations.

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True for both.
Solution verified.
One solution means consistent and independent system.
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