Question

Solve the following system of equations:

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

(3, 1)

(-1, 3)

(-1, -3)

(1, 3)

Answer 1

@SolomonZelman

Answer 2

\(\large\color{black}{ \displaystyle -2x + y = 1 }\)
\(\large\color{black}{ \displaystyle -4x + y = -1}\)

instead of subtracting them, which might be inconvenient because of sign-confusion, I would multiply one of the equations (which one, is up to you) times (-1).
THEN add the equations together.

Answer 3

I'm not sure about this one because I got, (-1,3)

Answer 4

may I ask you how did you get that?
I am not necessarily saying you are wrong, just want to see your work.

Answer 5

I subtracted 4x from both sides, oh... I did it wrong

Answer 6

alright, you wanted to do a substitution (for y) ?
well... elimination would be better here....

Answer 7

\(\large\color{black}{ \displaystyle -2x + y = 1 }\)
\(\large\color{black}{ \displaystyle -4x + y = -1 }\)

multiply the second equation times -1,
and re-write the system after that.

\(\large\color{black}{ \displaystyle -2x + y = 1 }\)
\(\large\color{black}{ \displaystyle 4x - y = 1 }\)

now add the equations together.

Answer 8

I don't get how that's going to give me the answer, can you tell me what I have to do first?

Answer 9

I am giving you all directions.

Answer 10

do you see "what" i did so far ?

Answer 11

yes

Answer 12

then tell me what is `(y) + (-y) ` equal to ?

Answer 13

0

Answer 14

y + - y = ?

Answer 15

yes 0

Answer 16

so, when you add the equations (ADD the X's , the Y's the numbers on the right sides of the equations, SEPARATELY).

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

Answer 17

okay

Answer 18

( -2x + y = 1)
\(\normalsize\color{black}{ \rm ^{^{\LARGE +}} }\) ( 4x - y = 1)
\(\large \color{black}{ \bf ^{ ^\text{___________________________}
} }\)

Answer 19

6x +0 = 1 ?

Answer 20

close

Answer 21

1 + 1 =?
-2x + 4x =?

Answer 22

you got 0 for middle term correctly.

Answer 23

1 + 1 = 2 and -2x + 4x = 2x since it is a negative 2 in the beginning

Answer 24

or is it -6x

Answer 25

yes
the result of addition of the 2 equations is

2x + 0 = 2

Answer 26

so you can already find the x.
x= ?

Answer 27

1

Answer 28

yes

Answer 29

x=1
and knowing that x=1, you can plug in 1 instead of x, into any of the initial (original) equations to solve for y.

Answer 30

I got y = 3

Answer 31

So is is (1,3) ? That's what I got. When I plugged in the 1 in the equations, I got 3. Is that right ?

Answer 32

yes

Answer 33

x=1
y=3

the solution is (1,3)

Answer 34

sorry for late replies, I am lagging

Answer 35

It's fine and thanks so much!

Answer 36

You are surely welcome!