Question 625686: please help me with this question it says i have to solve the system below graphically and indicate the method i use to plot the lines and show my work.... a. y=2x 2x+y=4 b. check by substituting the answer back into the orginal equations. thank you...
Answer by solver91311(16897) (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 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.
To check, take the -coordinate of your solution point and substitute for in either one of your equations, then take the -coordinate of your solution point and substitute for in that same equation. Do the arithmetic. If the result is a true statement, then the point is a solution of that equation. Repeat the process with the other equation.
If the point is a solution of BOTH equations, then it is a solution of the system of equations.
My calculator said it, I believe it, that settles it