Question

Can someone please explain substitution to me? I understand how it works, but could you maybe give me a fast, efficient, way of doing it without just wasting all your time guessing random numbers that won't work...? Example:

6x+4y=2,000

x+y=410

Thanks so much! I really appreciate the help! :)

Answer 1

substitution means replace one thing with another

in math, it means that you replace one expression with an equivalent expression or number

for example, if you are given x+2 = 5 then we can solve for x to get x = 3

to check this answer, we `substitute` 3 in for x. Ie, we replace x with 3

x+2 = 5

3+2 = 5 ... replaced x with 3

5 = 5 ... equation is true, solution x = 3 is confirmed

Answer 2

substitution is A way to solve a linear system algebraically. The substitution method functions by substituting the one y-value with the other.

Answer 3

But what if you had two different variables? Not just x but with y too?

Answer 4

when it comes to systems of equations, we can use substitution to solve

first pick on an equation that you can solve for x or y without involving fractions

the equation `x+y=410` is a good choice, so let's solve this for y


x+y=410

x+y-x=410-x

y = 410-x

now we `substitute` 410-x in for y of the first equation

\[\Large 6x+4y=2,000\]

\[\Large 6x+4\color{red}{y}=2,000\]

\[\Large 6x+4(\color{red}{y})=2,000\]

\[\Large 6x+4(\color{red}{410-x})=2,000\]

notice in the last step we replaced all of y with 410-x

from here, you would isolate x using the previous rules you learned in algebra

Answer 5

the reason why we're able to replace all of y with 410-x is because earlier we found y = 410-x

y and 410-x are equivalent, ie the same thing

Answer 6

jim seems like he got this since hes beating me to the questions

Answer 7

lml

Answer 8

Haha caution0, but thanks to both of you guys! It kind of pisses me off that I'm learning more from the internet in 5 minutes than in an hour at school...

Answer 9

lmao no problem ^.^