Question 699811: Hi,
the question is: solve each question by graphing. Graph each equation.
the two equations given are
1) 2x-2y=5
2) y=x-4
in the first equation y and x are on the same side, i only know how to do it when the equation equals y (like in the second equation) because, like in the second equations the x would be the slope and the -4 would be the y-intercept so in an equation like the first one i was wondering which one is slope and which one would be the y-intercept because i couldnt figure it out.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
First things first...you said "...in the second equation the  would be the slope and the -4 would be the  -intercept..." Both wrong. The slope is the coefficient on and the constant term is the -coordinate of the -intercept. An intercept is a point and a point is designated by an ordered pair. Hence a -intercept looks like ) where  is the constant term in the slope-intercept form of an equation of a straight line. On the other hand, none of that really matters in the solution of this problem. Follow the procedure below:
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.
Then again, if you insist on having both equations in slope-intercept form, then add  to both sides of your first equation and then multiply both sides by  .
Hint: Parallel lines have identical slopes.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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