Question

Can someone explain to me how to know when I need to use addition, subtraction, and multiplication when using the elimination method in algebra I am very confused? Explain with steps if possible.thanks

Answer 1

Explanation:

Okay when we use the elimination method we are solving two equations simultaneously, meaning that we have to variables that we dont know in two different equations and we cancel one out so we can solve for the other:

So heres an example:

2x + 3y = 19

4x + 15y = 35

Now we have two equations, and what we want to do is have one number with a variable in it to be equal and opposite to the other so when we add them they cancel. This is what I mean:

If we multiply the whole first equation by -2 we get

-4x - 6y = -38

Now notice that we have a -4x and a positive 4x and this is what we want because when we add them together that equals zero, meaning we got rid of that term to solve for y.

So lets add:

-4x - 6y = -38

4x + 15y = 35

9y = -3

Divide by 9

y = -1/3 (when you reduce)

Now to get the other answer we have to plug the value for y into either of the two equations that were given, ill choose the first one:

2x + 3(-1/3) = 19

2x - 1 = 19

Add 1

2x = 20

Divide by two

x = 10

There! Now we have both our solutions and we can say that for these equations

x = 10 and y = -1/3