SOLUTION: My algebra 2 teacher isn't very good at explaining how to do this. Its solving linear systems algebraically and I don't understand it what so ever. You have to figure out if its a

Question 774506: My algebra 2 teacher isn't very good at explaining how to do this. Its solving linear systems algebraically and I don't understand it what so ever. You have to figure out if its a system or whatever. Its hard. So the equation is this:
2x+5y=7
x+4y=2
Answer by sofiyac(983) (Show Source): You can put this solution on YOUR website!
There are multiple ways to solve it, elimination, substitution, graphing. We'll go with elimination since you didn't specify. In elimination the goal is to eliminate one of the variables. It doesn't matter which one you pick but there are "tricks" to picking an easier one. In order to eliminate a variable, in this case I pick x, you have to get one equation to have coefficient A (could be any number) and the other equation to have coefficient -A (same number but negative). So a lot of times in these problems you have to find common denominator between both equations for the variable that you pick to eliminate. So as I said we're looking to eliminate x, because it's easier. First equation has 2 Times x, which means in the second equation we need -2 Times x. So what we do first is multiply everything in second equation by -2. So i'm going to copy the first one as is and second one will be multiplied by -2.
2x+5y=7
-2x+4y=2 now you add the two equations, I just do it vertically as is
So we have 2x-2x which is 0 (that's why it's called elimination, we eliminated x variable). Then 5y+4y is 9y and 7+2 is 9. So when we add the two equations we get
9y=9 now we just solve for y by dividing each side by 9 so we have
y=1 now that we have y, we need to find x. You do that by plugging in y=1 into either of the two original equations. Doesn't matter which. I'm going to go with the second one because it'll cause less steps. So we have
x+4(1)=2 now we solve for x, so we simplify the left side and get
x+4=2 now we subtract 4 from each side of the equal sign and we get
x=-2
So the solution to this system of equations is (-2,1) (first you put the x value that we solved for, and in the second spot you put the y value, so that's how we got our solution). Solution in these problems is a point where both lines intersect.
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