Mathematics 26 Online
OpenStudy (anonymous):

y=4x x+y=5

OpenStudy (sandra):

hello

OpenStudy (sandra):

this is a classic "substituion" problem

OpenStudy (sandra):

the idea is that you want to take the value of a variable from one equation, and "substitute" that into the other

OpenStudy (sandra):

since you have two unknowns, you need two equations - which you have

OpenStudy (sandra):

so let's take y=4x and substitute it into the second equation

OpenStudy (sandra):

so x+y = 5 becomes x + (4x) = 5 (I just replaced y in the second equation with what the first equation asserted y to be)

OpenStudy (sandra):

that is called subsitution

OpenStudy (sandra):

so x+4x =5, 5x=5, and now divide both sides by 5 for the answer

OpenStudy (sandra):

so x = 1

OpenStudy (sandra):

now that you have x, you can substitute that back into either equation to get the value of y

OpenStudy (sandra):

so x+y = 5, and I know that x=1. so 1+y=5, 1-1+y = 5-1, y=4 (subtract 1 from both sides)

OpenStudy (anonymous):

i got up to x=1 then got confused on Y

OpenStudy (sandra):

ok great

OpenStudy (sandra):

well, think of x=1 as just another piece of information you now have, along with the original equations

OpenStudy (sandra):

so if x+y = 5 , and I already know x=1, then I can substitute the value of x in that first equation with what I know to be true

OpenStudy (sandra):

so 1 + y = 5

OpenStudy (sandra):

and then y=4

OpenStudy (sandra):

you can always check your work at the end of these problems too

OpenStudy (anonymous):

plug in 4x for y x+4x=5 5x=5 5 divided by 5 = 1

OpenStudy (sandra):

so our guess is that x = 1, and y = 4

OpenStudy (sandra):

if you stick those back into the original equations, do they hold true?

OpenStudy (anonymous):

yes

OpenStudy (sandra):

if they do, then you know you did it right

OpenStudy (anonymous):

ok. got it. thank u

OpenStudy (sandra):

np!