Question 429017: solve eah system of equation. If the system has no solution, say that it is inconsistent.
x-y=5
-3x+3y=2
Answer by IWork4Dessert(60)   (Show Source):
You can put this solution on YOUR website! When faced with a system of equations such as this, there are multiple ways to solve them based on personal preference. The two methods that work best with this one, however, are substitution and elimination. In substitution, you get one of the two variables on one side(alone, without a coefficient) and then plug in what it equals into the second equation. In elimination, you multiply one equation so that one of the variables has a coefficient that would make it cancel out the other equation's variable.
It's better to show than explain!
SUBSTITUTION:
x-y=5
-3x+3y=2
Now, you decide which equation would be better suited to substitution usually by seeing which equation has a variable that doesn't have a coefficient in front of it already. This would be x-y=5, in your case; it's more simplified. Let's solve for x first. Get the x alone.
x=y+5
Now you have what x equals, so plug it back into your second equation.
-3(y+5)+3y=2
Solve.
-3y-15+3y=2
Now you've hit a road block. -3y and 3y cancel out, which means that there's no variable left in your equation. Your answer? INCONSISTENT.
ELIMINATION:
Multiply one equation so that one of your variables can cancel out another. For example, we might want to try to cancel out the x's first, so you'd multiply the top equation by 3 to get 3x.
3x-3y=15
-3x+3y=2
You run into the same problem! Now both of your variables cancel out. INCONSISTENT.
Hope this helps!
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