Solve using the elimination method 7x + 7y = 7 x + 2y = 2 pleas explain I do not get this at all

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Solve using the elimination method 7x + 7y = 7 x + 2y = 2 pleas explain I do not get this at all

Mathematics
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ok let us go step by step
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
\[7x + 7y- 7 \therefore x+y =1 \therefore x=y-1\]

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7x+7y=7 x+2y=2 The goal is to eliminate the x's or the y's It is your choice
or you could mutiply -7 to the second equation
ok now i put in my two cents again. says "elimination" not "substitution" although i would use the second method as well
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
substituting that in equation 2 we have\[\begin {array} x x+2y=2 \\ y-1+2y=2 \\ 3y=3 \\ y=1 \end {array}\]
opps my bad
didnt read elimination sorry
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
ok I am so confused
ok I get it sorry didnt get it at first
so is it fine now?
Yes it is thank you so much I get it now i hope
if u have any doubt clear it =D all the best
Thank you :)
I thought it would be 2y-y=2/1
there for y=2
I will do it for you using elimination
i just need the process explained to me it just is not clicking im sorry
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
ok this makes since to me thank you
so this would be and infanite solution correct because it would graph as the same line not two intersecting line?
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
No this is one solution because we were able to find the point of intersection
oh ok so what would a infanite solution look like?
sorry to ask so many questions, but I really want to grasp this and I am having a really hard time
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
yes I see
No solution is 2 parallel lines, they never cross. look for same slopes y=2x+3 y=2x+6
thank you so much for explaining this I understand it so much better now than i did from the book
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)
Thank you so much
Anytime :)

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