Question

Systems of equatons: Solve for x and y
y=2x+9
y=x-5

Answer 1

multiply the second equation times -2 or -1 and add the equations

Answer 2

when subtracting equations might be confusing, multiply by negative and add, to avoid confusion.

Answer 3

or you can use a matrix, which would be fun too.

Answer 4

Jeez I am only in 8th grade. This is freaking Confusing xD

Answer 5

@SolomonZelman So when i multiply the 2nd one i got -2x +10. Is that correct?

Answer 6

when you multiply the second equation times -2 , you have:

\(\large\color{slate}{\displaystyle y=x-5}\)

\(\large\color{slate}{\displaystyle \left[y\times -2\right]=\left[x\times -2\right]\left[-5\times -2\right]}\)

\(\large\color{slate}{\displaystyle -2y=-2x +10}\)

correct!

Answer 7

Now, add the equations together:

\(\large\color{slate}{\displaystyle ~~~-2y~=~-2x~~+10}\)
\(\large\color{slate}{\displaystyle ^{^{\LARGE+}}~~~~~~y~~=~~~2x~~~~~+9}\)
\(\Large\color{slate}{\displaystyle ^{\text{______________________}}}\)

Answer 8

do each thing separately.

1. Add the y's
2. Add the x's
3. Add the numbers

and re-write the equation.

Answer 9

y= 19
did i do that right?

Answer 10

almost.

Answer 11

Wait its -y = 19

Answer 12

yes.

Answer 13

and if -y=19 then y=? (can you tell me that?)

Answer 14

(multiply both sides times -1 to find what y is)

Answer 15

-19?

Answer 16

yes
y=-19

Answer 17

okay now I need to find x

Answer 18

Now, after you found y, you can solve for x without a problem by plugging your y-value (which is -19) into ANY of the ORIGINAL EQUATION.

Answer 19

\(\large\color{slate}{\displaystyle y=2x+9}\)
\(\large\color{slate}{\displaystyle \color{red}{-19}=2x+9}\)
and then sovle for x.

Answer 20

solve*

Answer 21

\(\large\color{slate}{\displaystyle 19=2x+9}\)

\(\large\color{slate}{\displaystyle 19\color{red}{-9}=2x+9\color{red}{-9}}\)

\(\large\color{slate}{\displaystyle 10=2x}\)

and then, \(\large\color{slate}{\displaystyle x=?}\)

Answer 22

x= 5

Answer 23

yes

Answer 24

Thank you @SolomonZelman Can you help me with one more?

Answer 25

So your solution is
x=5
y=-19

In other words, your 2 equations
y=2x+9
y=x-5
intersect at a point (5,-19)

Answer 26

yes, I can help with another one.

Answer 27

y= x - 2
2x - 3y = -5

Answer 28

yes.
The way they are writing the system, they are wanting you to substitute (do 'substitution').

Answer 29

Your first equation \(\large\color{black}{ \displaystyle y= x - 2 }\), is telling us, that (in this case) \(\large\color{black}{ \displaystyle x - 2 }\) is the same exact thing as \(\large\color{black}{ \displaystyle y }\).

That means wherever you see a \(\large\color{black}{ \displaystyle y }\) in the other equation, you can replace this \(\large\color{black}{ \displaystyle y }\) by \(\large\color{black}{ \displaystyle x - 2 }\).

Answer 30

The way this will happen is as follows:

your second equation.
\(\large\color{black}{ \displaystyle 2x - 3y = -5 }\)

replacing the ` y ` with ` x+2 `

\(\large\color{black}{ \displaystyle 2x - 3(\color{blue}{x+2}) = -5 }\)

Answer 31

See what is going on here up to this point?

Answer 32

Yeah

Answer 33

Wait so x = -1

Answer 34

@SolomonZelman are all of these in the right quads?
http://gyazo.com/d89273d94b017f8d6a9f0a1fe739ffb4

Answer 35

you can graph the equations on
https://www.desmos.com/calculator

and tell me in which quadrant the intersection point occurs.

Answer 36

is this graphing calculator good ?

Answer 37

2x-y=-2 and x - 2y = 5 intercept at points (-3,-4)