Question

What is the solution to the system of equations?
4x+y=2
x-y=3

Answer 1

add the equations to each other, this will help you eliminate one parameter (the y).

Answer 2

how do you add them?

Answer 3

\(\large\color{black}{ \displaystyle 4x \quad+y\quad=2 }\)
\(\large\color{black}{ \displaystyle ^{\huge ^+} \quad x\quad-y\quad=3 }\)
\(\LARGE \color{black}{ \displaystyle ^\text{_____________} }\)

Answer 4

\(\large\color{black}{ \displaystyle 4x+x=\quad ? }\)

\(\large\color{black}{ \displaystyle y+(-y)=\quad ? }\)

\(\large\color{black}{ \displaystyle 2+3=\quad ? }\)

Answer 5

4x+x= 4?

Answer 6

Don't ask why I ask, just answer if you can, please.

Answer 7

4 + 1 = ?

Answer 8

5

Answer 9

Just as: 4 +1 =5
So is: 4x +1x =5x

Answer 10

(note that when you say "x" you really mean "1x")

So, 4x+x=?

Answer 11

5x

Answer 12

Yes, and 3+2=?

Answer 13

5

Answer 14

Very nice...

Answer 15

y - y = ?

Answer 16

1 - 1 = 0 or,
(Anything) - (Anything) = 0

Answer 17

y+(-y)=0

Answer 18

yes

Answer 19

\(\large\color{black}{ \displaystyle \color{red}{4x} \quad\color{green}{+y}\quad=\color{blue}{2} }\)
\(\large\color{black}{ \displaystyle ^{\huge ^+} \quad \color{red}{x}\quad\color{green}{-y}\quad=\color{blue}{3} }\)
\(\LARGE \color{black}{ \displaystyle ^\text{_____________} }\)

\(\large\color{black}{ \displaystyle \color{red}{5x} \quad\color{green}{+0}\quad=\color{blue}{5} }\) <─ the result of
adding these 2 equations

Answer 20

Does everything make sense so far?

Answer 21

yes

Answer 22

To say:
5x +0 = 5

Is the same as saying:
5x = 5 (Because adding zero makes no difference)


And now you are able to solve for x (by dividng both sides by 5).

Answer 23

x=1

Answer 24

Very good!

Answer 25

x=1.

You can substitute this solution for x into any of the original equations to solve for y.

Answer 26

Lets use the 2nd equation:
x - y = 3

YOu are given that x=1, so you can re-write theis equation as:
1 - y =3

Answer 27

Does everything make sense so far ?

Can you solve for y?

Answer 28

yes

Answer 29

1-y=3 y = -2

Answer 30

yes,
x=1 and y=-2

Perfect!

Answer 31

You made it !

Answer 32

on the question i need hep with it is giving me cordintes that i have to fill in would that be (5x,5)

Answer 33

Your coordinates are in the form of (x,y)

Answer 34

Plug in the x-solution for x, and the y-solution for y.

Answer 35

(5,5)

Answer 36

is that correct