Question

Solve using the elimination method 7x + 7y = 7

x + 2y = 2 pleas explain I do not get this at all

Answer 1

ok let us go step by step

Answer 2

step one is do divide the first equation by 7 to make your life simpler. you get
\[x+y=1\] and now i shut up

Answer 3

\[7x + 7y- 7 \therefore x+y =1 \therefore x=y-1\]

Answer 4

7x+7y=7
x+2y=2
The goal is to eliminate the x's or the y's
It is your choice

Answer 5

or you could mutiply -7 to the second equation

Answer 6

ok now i put in my two cents again. says "elimination" not "substitution" although i would use the second method as well

Answer 7

Technically the method does not matter but since it did say elimination it is better to cancel out the x's or the y's
I am choosing to get rid of the x's by multiplying -7 to equation 2

Answer 8

substituting that in equation 2 we have\[\begin {array} x x+2y=2 \\ y-1+2y=2 \\ 3y=3 \\ y=1 \end {array}\]

Answer 9

opps my bad

Answer 10

didnt read elimination sorry

Answer 11

ok in this you can solve by subtracting the two equations that is x+y=1 and x+2y=2.. you get 2y-y=2-1 therefore y=1

Answer 12

ok I am so confused

Answer 13

ok I get it sorry didnt get it at first

Answer 14

so is it fine now?

Answer 15

Yes it is thank you so much I get it now i hope

Answer 16

if u have any doubt clear it =D all the best

Answer 17

Thank you :)

Answer 18

I thought it would be 2y-y=2/1

Answer 19

there for y=2

Answer 20

I will do it for you using elimination

Answer 21

i just need the process explained to me it just is not clicking im sorry

Answer 22

7x+7y=7
x+2y=2

7x+7y=7
-7(x+2y=2)

7x+7y=7
-7x-14y=-14
add equations together

-7y=-7
divide by -7 to both sides
y=1

x+2y=2
x+2(1)=2
x+2=2
-2 both sides
x=0

solution x=0 and y=1

Answer 23

ok this makes since to me thank you

Answer 24

so this would be and infanite solution correct because it would graph as the same line not two intersecting line?

Answer 25

Another name for this method is called multiplication and addition method
First you pick a number to multiply one of the equations
then you add both equations together
goal is to get rid of the x's or the y's
that is why is is called elimination.
If you wanted to get rid of the the y's instead
you would have to multiply 2 to the first equation
and then -7 to the second equation
this will produce 14y and -14y and then you would have solve for x first.
Many ways to eliminate x's or y's

Answer 26

No this is one solution because we were able to find the point of intersection

Answer 27

oh ok so what would a infanite solution look like?

Answer 28

sorry to ask so many questions, but I really want to grasp this and I am having a really hard time

Answer 29

infinite solutions is the same line given in multiple form
example
x+y=4
2x+2y=8
did you notice they are the same
I only multiply 2 to the original equation

Answer 30

yes I see

Answer 31

No solution is 2 parallel lines, they never cross.
look for same slopes
y=2x+3
y=2x+6

Answer 32

thank you so much for explaining this I understand it so much better now than i did from the book

Answer 33

The number of solutions is determined by the number of times the equations cross:
One solution means they cross in one place (X,Y)
No solution means they do not cross (Parallel lines)
Infinitely many solution means they cross in many places (because they are the same line)

Answer 34

Thank you so much

Answer 35

Anytime :)