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How to Determine When a System of Equation Has no Solution by Elimination

so on the next process Rebecca that you

missed is if you guys look at this

equation this one's a little bit

different so there's something special

about that last one because we had a

variable had a coefficient of 1 right

and we like that Briana because i had a

coefficient 1 it was easy to solve for

that variable however and when you have

a case like this we don't have a

variable has a coefficient of 1 if you

still like substitution you can still

apply substitution Jordan but it comes a

little bit more difficult that's why we

like to look at using elimination which

we looked at so when apply an

elimination basically what we're doing

rather than solving for one variable and

plugging what that expression is into

the other equation basically what we're

doing is we're adding its or subtracting

the two equations so to add or subtract

it only makes sense to add or subtract

equations is when you have the variable

the equations with coefficients that are

exactly the same so I look at make sure

my variables are aligned which they are

then I look at the coefficients of the

variables to see if they're the same

well the coefficients of X's aren't the

same nor other coefficients of the why

the same all right so i need to say all

right well which one doesn't matter

which one is going to have the smaller

coefficient are the least common

multiple well 6 forget about the

negatives three and six ave least common

multiple of six and two and four have a

least common multiple of four so any

either way to get them to be the same

all i need to do is multiply my top

equation by 2 so i'm going to do that so

i multiply the top equation by 2 and

when i do that i obtain 6x minus 4y

equals 10 and then my bottom equation is

going to remain the same negative 6x

plus 4y equals 7 now usually when we're

doing elimination we're only eliminating

one variable at a time but as you guys

notice when i multiply this now both of

my variables have coefficients that are

exactly the same you guys see that and

since the coefficient is one's positive

ones negative should I add the equations

or subtract the equations to eliminate

to get 20 I should just add them

we'll see that you you can x like if

these were both positive i would say

multiply this by negative 2 because then

that would be negative 6 positive 6 but

you already have a negative 60 make one

positive one negative and that's fine

now let's go ahead and add them 6x plus

negative six x is 0 X negative 4y plus

positive 4 y is 0 y equals 17 0 X plus 0

Y is 0 equals 17 so I look at that and I

determine all right this system of

equations is it has a false statement it

doesn't tell me what x is equal to or

what y is equal to it gives me a false

statement since they give me a false

statement kijan this is a no solution

there is never going to be an

intersection that is going to be true

for either of these equations so

therefore it's no solutions that if

you're going to look at the graph of

that it represents