Question

FAN AND MEDAL


1. Solve the following system of equations: (1 point)
-2x + y = 1
-4x + y = -1


(3, 1)
(-1, 3)
(-1, -3)
(1, 3)

Answer 1

well the idea is that you need to eliminate one of the variables by combining the two equations together.

Answer 2

here's what you do: you see that in both equations you have +y right?

Answer 3

yes

Answer 4

would you take away one y?

Answer 5

let's chose to get rid of y. what number if multiplied by y would result in both y's canceling out or resulting in their sum being zero

Answer 6

1?

Answer 7

almost it's -1 you see why?

Answer 8

oh cause it is positive!

Answer 9

okay so now. check this out

Answer 10

we must multiply one of the equations by -1. everything because we need to ensure that when we do something to an equation it's done to everything


let's pick the top equation we multiply everything by -1

-1*(-2x+y = 1) becomes

= -1*-2y+ (-1*y) = -1*1

2x-y = -1

Answer 11

oh i see now do we do that to the other equation too?

Answer 12

now we get this:

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

Now the point of this is that when we ADD the two equations together y cancels out.

so try adding these equations together and then tell me what you get?

Answer 13

-2x=-2?

Answer 14

yep :)

Answer 15

so now, you know what x is

Answer 16

and then do you divide by -2?

Answer 17

yep so what's our x value?

Answer 18

-1?

Answer 19

remember -2x = -2

x = 1

because -2*1 = -2

Answer 20

ohhh yeah

Answer 21

so D is the correct answer?

Answer 22

now how do you think we would find Y?

Answer 23

We're almost done

Answer 24

by putting 1 into the equation?

Answer 25

so let me show you something:

we know that x = 1 right?


to find y all we need to do is plug in x =1 into one of the equations


-2x+y = 1

try doing that and showing me what you get.

Answer 26

-2(1)+y=1
-2+y=1
+2 +2
y=3
is this right?

Answer 27

so you got 3 for y?

Answer 28

=) yep

Answer 29

@adll23 the most important step is eliminating the variable

Answer 30

yes it is:) YAYAYAY thank you so much! you made it so much easier for me!

Answer 31

first ask yourself what number must i multiply one equation by such that when I add them both together, one variable cancels out

Answer 32

kk

Answer 33

Also multiplying a number by an entire equation is kind of like the same thing you aren't doing something to it.

so if you multiply one number say y by -1 it has to be done to the entire equation

that's all. :)

Answer 34

well i should mean you aren't changing anything by doing that

Answer 35

yes! thank you so much for the help, Photon:)

Answer 36

no problem anytime :)

Answer 37

if you want you can try to find (x and y) in this problem

2x+y = 3
x+y = -2