5x+6y=65 3x+2y=25

Answer 1

In this type of problem, the easiest thing is to make either the x or y variable in each equation equal to each other. In the first equation you have 6y while in the second equation you have 2y. You can make them equal by multiplying the entire 2nd equation by 3. The second equation would then become 9x+6y=75.

So, if you rearrange the two equations, you know that in the first equation 6y=65-5x and in the second equation 6y=75-9x therefore: 65-5x=75-9x.

Now you can solve for x. First, you need to get the x's on the same side, so add 9x to each side to get 65+4x+75. Then subtract 65 from each side to get 4x=10, so x=10/4 or 2.5. Now you can plug in for x and solve for y.

Answer 2

Remember, there are three methods to solving a system of equation: graphing, substitution, and elimination.

5x + 6y = 65

3x + 2y = 25

For elimination, (the most common method), we need to eliminate one of the variables. It is easier to eliminate y since 6y is a multiple of 2y. Don't forget that we want to ELIMINATE the variable. So, we need to find the multiple that makes the following true:

6y + (___)(2y) = 0

Whatever goes in the blank is the value that the second equation must be multiplied by. Then we can add the two equations.

Adding these equations now will allow you to solve for x. After finding x, plug x back into one of the original equations. It doesn't matter which one!

Now you have an x and a y value. How do we express our answer? The same way we would if we were using the graphing method! We write our answer like a point. That is, (x , y).