How do I solve equations using the substitution method?

Question

I've never been good at algebra. Even through highschool I always had to go for help. I'm trying to figure out the substitution method so I can teach my 13-year-old niece who is living with me. I've started homeschooling her and I haven't the slightest clue how to explain this to her.

1. 3x + y = 5

2x - y = 10

2. y = 5 - x

1 = 4x + 3y

3. 2x + y = -92

2x + 2y = -98

4. 4x + 3y = 13

x + y = 4

I'd truly appreciate it if someone could show me step by step how to do these. :)

Thank you for anyone who is mature about this question.

Answer 1

I will try to show you #2

y=5-x

Substitute y in the next equation

1 = 4x + 3(5-x)

Now all you have to do is solve x to find out y

1 = 4x + (15-3x)

1 = 4x +15 - 3x

1-15 = 4x-3x

-14 = x

Now plug the x value into the 1st equation

y = 5 - -14 which is 5+14

y=19  so now plug that in to the 2nd equation does it work?

1 = 4(-14) + 3(19)

1 = -56 + 57

It works. It has been a long time - I now have a head ache.

That is how replacement is done. If you have any questions, I will try to answer them.

Answer 2

Our modern society revolves around math, so you should be concerned about your teaching skills. One of the first things to 'teach' your student is to Google for help.

Try Googling ' math substitution method' and see what comes up.

Remember ONE thing about math; The rules NEVER change [except maybe when you get to Quantum Mechanics], so although it's a bit complicated, it's never difficult.