Thread: Systems of Equations

I am entering precalculus but in order to finish the summer packet, I have to go all the way back to algebra. I need some refreshing on system of equations.

If you could explain how to do these problems and give me a summary of how to do the different methods, it would be extremely helpful.

These are the specific questions I am having trouble with, if you explain how to do them it would be a big help. Thanks.

1) 5x+4y=6 -2x-3y=-1

2) -2x+y=8 y=-3x-2

Any help would be appreciated, thanks in advance.

Originally Posted by Mp5xm8

2) -2x+y=8 y=-3x-2

One method is substitution. You take one equation and solve for one of the variables. I picked the second problem because the second equation is already solved for one of the variables (y). You plug this into the 1st equation for y like this:
-2x + y = 8
-2x + (-3x - 2) = 8
-5x - 2 = 8
-5x = 10
x = -2

Then you take this result and plug it into the 2nd equation:
y = -3x - 2
y = -3(-2) - 2
y = 6 - 2
y = 4


01


EDIT: too early in the morning...

Thanks, for your explanation, now i just need some help with the other equation.

One method for exercise (1) would be addition (or elimination). You could, for instance, multiply the first equation by 3 and the second by 4, and add the results.

What method(s) did you try, and where did you get stuck?

Please be complete. Thank you!

Well I don't remember anything of how to solve systems of equations, so i came here. What I don't understand about the specific method you talked about is how you can multiply the equations by different numbers, doesn't that change the answer? Or is there some way to decide which numbers to multiply by?

From your question, it sounds as though, in addition to not looking at the systems-of-equations lesson provided earlier, you might not be familiar with how to solve linear equations...? (One of the first rules one learns for solving linear equations is that one can multiply or divide through, and this won't change the answer. You seem not yet to have heard of this.)

It would probably be wise first to learn how to solve linear equations. In particular, note the "one-step multiplication" sorts of exercises, in which the solution is found precisely by multiplying the equation by some value.

Once you're familiar with that, study at least two lessons on solving systems of linear equations by addition or elimination (two names for the same thing). Then the step-by-step instructions, provided earlier, should make a lot more sense.

In my algebra class we spent very little time on systems of equations, I knew how to do them, but I have forgotten now, thank you for the help.