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Question 592175: Hello! I tried using one of your solvers, but it did not work because there was not a subtraction option.
Anyways, I need to solve this system of equations by graphing;
2x - y = 5
x + 7 = 7
I did it by addition/subtraction AND substitution and got ( 3,4 ), but when using the Systems of Equations Graphing Solver, as I had stated, there was no subtraction option, so I could only use addition for my first system, thus making everything wrong. Please help me! I'm doing this for a project that is due TOMORROW and I need prompt help! It is the last part of the project, so I'm not very worried as I have created everything else correctly. Thank you for your time in advance!!
- Cameron
Found 2 solutions by scott8148, solver91311:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! something is amiss, because (3,4) does not work in either of the equations [(4,3) works in the first equation]
also; x + 7 = 7 becomes x = 0, which is the y-axis
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assuming multiple typos... 2x - y = 5 becomes y = 2x - 5 ; and x + y = 7 becomes y = 7 - x
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. Note: For your second equation, since it represents a vertical line where all of the ordered pairs have the same x value, there is only one value of x that will make your second equation a true statement.
Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results. Again, since your second equation is a vertical line, ANY y value you like will satisfy the equation. So pick a value, it doesn't matter.
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 both lines graph to the same line, then the solution set is infinite, i.e. every ordered pair that satisfies one equation will satisfy the other. If the lines are parallel, then the solution set is empty.
A consistent system has at least one solution.
An inconsistent system has no solutions.
An independent system has exactly one solution.
A dependent system has infinitely many solutions.
Therefore a system can be either consistent and independent, consistent and dependent, or inconsistent.
John
My calculator said it, I believe it, that settles it
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