Question

Can someone help me with simultaneous equations when they are like this

2x+3y=21
2x-2y=6

I dont get it when theres a + and -
i can do it with + and +

Answer 1

easier with a "+" and "-" multiply the first one by 2 and the second one by 3. then add and the "y" will drop out leaving only an equation in x

Answer 2

Multiple bottom equation by negative one and get: -2x+2y=-6 Now add the first equation to that result 2x+3y=21
and get........................................................................ 5y = 15
Divide by 5 and get y = 3 Find x by substituting into any equation that contains an x.

Answer 3

thnx

Answer 4

\[2\times (2x+3y)=2\times 21\]
\[4x+6y=42\]
\[3\times (2x-2y)=3\times 6\]
\[6x-6y=18\] add to get
\[10x=60\] and so
\[x=6\]

Answer 5

@satellite73

i dont understand your method maybe give like steps and why do i do it x3 and x2.

@Mertsj thnx for the help but you have not told me y u do it like that as i want a concept so when i get any equation like that i can work it.

Answer 6

i get why now but like what i said to Mertsj how will i know what to do for any random one

Answer 7

i look at the y terms. first one has
\[3y\] and the second has
\[-2y\] so i ask the question "who can i match them up so that if i add the y will be gone?"
one is positive and the other is negative so that is a good start. and the least common multiple of 2 and 3 is 6 so i match them up so that one will be
\[6y\] and the other
\[-6y\]

Answer 8

you have to figure that out for yourself, but you use the least common multiple to make them match up

Answer 9

so u make the same coefficients but how do u work with the +6 and -6
maybe im not making myself clear

Answer 10

My main problem was i know how to do it but i cant get past it when theres a plus and - in the other so +6y and -6y
oh i just got it while writing it down so basically they cancel each other out so then u basically work out the x

Answer 11

Thnx alot guys i think i got it

Answer 12

yes good. the plus and minus is an asset, not a indifference because it makes them add to zero

Answer 13

Here is what you want to do: Your goal is to make the coefficient of x in the first equation to be the opposite of the coefficient of x in the second equation. Then when you add the two equations, the coefficient of x will be 0 and 0 times x is 0 so the x disappears.

Sometimes it will be easier to make the coefficient of y in the first equation be the opposite of the coefficient in the second equation. Then when you add the two equations, the coefficient of y will be 0 and 0 times y is 0 so in that case, the y will disappear.

Answer 14

Thnx Again