Question 708263: This is systems by elimination and i was out sick for a week and a half i have no clue whee to even start. Please help :(
-7x-3y=12
9x+3y=-12
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! The elimination method involves:- Setting up the equations so that opposite variable terms are lined up. This can be the hardest part. Sometimes terms have to be rearranged to line up like terms. Sometimes one or both of the equations will need to be multiplied by some number to create opposite terms.
- Adding the two equations together. The lined up opposite variable terms will cancel each other out resulting in an equation with just one variable.
- Solve the one-variable equation.
- Use the solution to the one-variable equation to find the second variable. Substitute for the solved variable in one of the original equation and solve for the second variable.
- If you want/need to check, then substitute both variables into both of the original equations. If either equation fails to check out (i.e. be a true statement) then a mistake was made somewhere.
Let's see this in action.
-7x-3y = 12
9x+3y = -12
1. Line up the opposites
Your y terms, -3y and 3y, are opposites and they are lined up with each other. So are all set.
2. Add the equations.
2x + 0 = 0
3. Solve the one-variable equation.
2x = 0
x = 0
4. Use the solution above to find the other variable. Substituting for x into the first equation we get:
-7(0)-3y = 12
0-3y = 12
-3y = 12
y = -4
5. Check
-7(0)-3(-4) = 12
9(0)+3(-4) = -12
(I'll leave it up to you to finish the check if you want one.)
P.S. Most of the time, when you add the equations only one variable disappears. (In our problem the y terms disappeared.) Sometimes both variables disappear! In other words you only have numbers (no variables) left). In this case the equation is either a true statement (like 34 = 34 or -0.4 = -0.4 or 0 = 0, etc.) or a false statement (like 4 = 3 or 1/2 = 9 or -3 = 3, etc). If the statement is...- TRUE. This means that the two equations were actually equations for the same line! This means the lines, in effect, lay on top of each other. Every point that fits one equation will fit the other one, too. This means they intersect at every point! In short, this means that there are an infinite number of solutions to the system (not just the usual single ordered pair).
- FALSE. This means the lines are parallel and do not intersect at all. In short, this means there are no solutions to the system.
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