300
Solve the system:
x=y+3
2x-y=5
What is (2,-1)?
Reason: There are three basic ways to solve this. The first way is by graphing both lines. The problem with graphing is that sometimes it is hard to tell where the two lies intersect, if the intersecting point isn't whole. In this case, there wouldn't be any problems because both coordinates are whole numbers. The second way is through substitution. The first step in substitution is getting one of the variables in one of the equations by itself. We ca skip this step in this system because x=y+3 already has x by itself. Now, we have to substitute y+3 for x in the other equation giving us, 2(y+3)-y=5. After applying the distibutive property, we get, 2y+6-y=5. Now, we must add like terms, which in this case is the 2y and the y. So, our equation becomes y+6=5. To get y by itself, we have to subtract 6 from both sides, and we get, y=-1. We still aren't done. Finally we have to find the value of x, so we substitute -1 for y in the first equation, add like terms, and we get x=2. The final way we could solve is through elimination. To do that, we must first put the first equation into standard form. To do that, we have to subtract y from both sides, and we get x-y=3. Now, we have to add or subtract the equations to get rid of one variable. In this case, because neither y have a coefficient before them, that is the easiest variable to use (x would require multiplying the entire first equatio by 2). Because they are both negative, we are going to subtract because subtracting a negative is like adding a positive. After we subtract, our equation becomes, -x=-2. Since -x=-2, we know that x=2. Now, we go back to either one of the equations, and substitute 2 for x. After you've done that, solve the equation. You should end up with -1 for y, but ALWAYS check your math!