Find 2 solutions to the equation 3x+5y=10. Write the solutions as ordered pairs.

This is on my math study guide for our final and she already took up our text books. please help me!

If you plot the graph of the equation

2x+5y=10
it represents a straight line, which in turn is made up of an infinite number of points.
If you substitute a value of x or y in the equation, then you end up with an equation containing a single unknown for which you can solve easily.
For example, let y=1, then
2x+5(1)=10
2x+5=10
2x=5
x=2.5
Thus (2.5, 1) will be one point on the graph.
You can repeat as many times as you wish to get the number of points you want on the graph. If you plot all those points, they should all fall on a straight line, because the original equation is a linear equation in x and y.

Now all you need to do is to use the equation your teacher gave you and follow the same procedure.

Here what the graph of the equation should look like:

http://i263.photobucket.com/albums/ii157/mathmate/3x5y.png

whenx=-2. 3(-2)+5y=10, -5+5y=10,+5y=5+5,+5y=10,y=+10

To find solutions to the equation 3x + 5y = 10, we can use a method called substitution or elimination. I will explain both methods, and you can choose which one you prefer.

Method 1: Substitution
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the equation for x:
3x + 5y = 10
3x = 10 - 5y
x = (10 - 5y) / 3

Step 2: Substitute the expression for x in the other equation:
3x + 5y = 10
3((10 - 5y) / 3) + 5y = 10
10 - 5y + 5y = 10
10 = 10

Since the equation resulted in a true statement (10 = 10), we can conclude that the system of equation is dependent, and there are infinitely many solutions. This means that any ordered pair (x, y) is a valid solution.

Method 2: Elimination
Step 1: Multiply one or both equations by constants such that the coefficients of x (or y) will cancel each other when we add/subtract the equations. Let's multiply the first equation by 5 and the second equation by 3:
5(3x + 5y) = 5(10)
15x + 25y = 50
3(3x + 5y) = 3(10)
9x + 15y = 30

Step 2: Subtract the second equation from the first equation to eliminate x:
(15x + 25y) - (9x + 15y) = 50 - 30
15x - 9x + 25y - 15y = 20
6x + 10y = 20

Step 3: Divide the equation by 2 to simplify:
(6x + 10y) / 2 = 20 / 2
3x + 5y = 10

As you can see, the result is the same equation we had initially. This indicates that the system is dependent and has infinitely many solutions. Therefore, any ordered pair (x, y) is a valid solution.

To summarize, the equation 3x + 5y = 10 has infinitely many solutions, and any ordered pair (x, y) will satisfy the equation.