Question

2x-1y=8
1x+2y=9

Answer 1

substition or elimination

Answer 2

well what does x equal

Answer 3

you can use any method other than matrices

Answer 4

ok which one do you prefer for this problem :)

Answer 5

elimination if thats ok

Answer 6

sure

try to make either x, or y the same coefficient in both equations
the sign does not matter, just the value

Answer 7

okay hold just asec

Answer 8

you can multiply an equation by some number: multiply every term with this number left and right to keep what equation states the same.

Answer 9

im a little confused right now

Answer 10

no problem

if you have some equation,
example: 2x+1 = y

then you can multiply everything by 3 left and right, and get
example: 6x+3 = 3y

the "balance" of the equation is still the same,
just the values are all bigger.

Answer 11

if this is clear, you know that you can multiply every term by some number
whenever it makes sense to you. it's a valid operation

Answer 12

so to get -1y to match 2y we would multiply it by -2?

Answer 13

YES EXACTLY

Answer 14

alright so we would get 2x+2y=-16?

Answer 15

2x was not changed: every term must be multiplied, every single one
if they're with a + between them, they count as seperate terms

then they both need separate, treatment

Answer 16

8 was treated (correct)
-1y was treated (correct)
2x was LEFT OUT !!ERROR!!

Answer 17

so 4x+2x+-16

Answer 18

uh uh uh, 2x times -2 changes the sign of x :)

Answer 19

oops yea so -4x+2y+-16 :(

Answer 20

very good

Answer 21

ok so what is the next step?

Answer 22

now, we can subtract one from the other to ELIMINATE Y

Answer 23

1x +2y = 9
-( -4x +2y = -16 )
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Answer 24

2x-1y=8....Eq:1
1x+2y=9....Eq:2
by substitution method
taking Eq:1 and separate x
2x=8-y
x=8-y\2.....Eq(3)
now put Eq:3 in Eq:2
8-y\2+2y=9
by the L.C.M
\[\frac{ 8-y+4y }{ 2 }=9\]
8-3y=18
-3y=18-8
-3y=10
y=-10\3
now put the value of y in Eq 3
\[\frac{ 24-10 }{ 3 }\2\]
14\6
7\3
x = 7\3 ,, y =-10\3

Answer 25

so the subtraction just turns around the sign of every term:
then we can add:

1x +2y = 9
+4x -2y = +16
-------------

Answer 26

it turns out that adding the -1 is the same as subtracting it

9 minus 4 = 5
9 plus -4 = ....5.

that's why the method above works (subtracting by adding sign changed)