Question

Have to study all day and night to pass a state test next Tuesday! Help & Explain! Also is there an easier way of solving without graphing?

Solving Systems by Graphing:

Solve each system by graphing.
y= 2x
y= -2x + 8


Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.
y= x + 3
y= x -1

Answer 1

See WolframAlpha's graph of the first problem:

http://www.wolframalpha.com/input/?i=y%3D2x%2C+y%3D-2x%2B8+

The lines intersect at (2, 4) which is your solution.

Next, the second set of equations:

http://www.wolframalpha.com/input/?i=y%3Dx%2B3%2C+y%3Dx-1

There is no solution because the lines do not intersect.

Answer 2

Well, I need an explaination. Not just the full answer. I have a STATE test on Tuesday and I really need to pass it @Rav .

Answer 3

Okay, here you go:

The solution means the point at which equation 1 = equation 2. That means, for the first problem, the point at which 2x = -2x + 8 = y. On a graph, you can see the solution by looking at the point where the lines intersect. For this set of equations that point is (2, 4), which means x = 2 and y = 4. Now let's test it: 2(2) = -2(2) + 8 = 4, which is correct.

Now, the second one is two parallel lines. Parallel lines never intersect, therefore there is no point at which equation 1 = equation 2, so there is no solution.

Answer 4

Okay so what about this equation which is kind of like the first one but have fractions:

y= 1/2x + 7
y= 3/2x + 3

Answer 5

Just draw it on graph paper or put it into WA:
http://www.wolframalpha.com/input/?i=y%3D1%2F2x%2B7%2C+y%3D3%2F2x%2B3

Solution: x = 4, y = 9

Answer 6

Remember to draw a line on a graph start at y=0, solve for x, and plot points at y=1, y=2, etc, then draw a line through it.

Answer 7

This doesn't make any sense to me what so ever.....

Answer 8

Also I am not so good at math. At all.

Answer 9

A function is an equivalency. It's just saying: When x is (some number), y is (some number) times (some operation). So for example y = 2x, means when x is 0, y is 0, when x is 1, y is 2, et cetera. You can draw the function on a graph by deciding what you want x or y to be, then put a point on that graph at the coordinates you find. For any function f(x), there is at least one y such that y = f(x). So that means there is at least one point on a graph at (x, y).

Now to draw the graph, usually you have a computer do it but if it's a straight line, then it's very easy. With a straight line you only need 2 points on the graph, then draw a line that crosses both those points. So when you have a function f(x) and you want a y such that y = f(x), you just decide y = 0 (because 0 is easy to work with), and then you put a point on the graph where x = 0, therefore y = f(0) = ?. So if y = f(0) = 2 * 0, then y = 0. So the origin (0, 0) is a point on your line. Then, put in x = 1: y = 2*1 = 2, and (1, 2) is a point on your line. Then draw the line so that it goes through both those points. Now let's say g(x) is another function, y = x + 1. Then at x = 0: y = 0 + 1 = 1, and (0, 1) is on that line. Then at x = 1: y = 1 + 1 = 2, so (1, 2) is on that line. Now remember y = 2x also has (1, 2) on it. So the two lines intersect at (1, 2) which is their solution. Since they are straight lines, there are only three possibilities: either the lines are parallel (meaning they never intersect), or they intersect at one and only one point, or they are the same line. So if you find one solution and the equations are different, then you know that is your only solution.

Does this help?

Answer 10

Yes. Thank you.