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Rachel98
 3 years ago
I need help getting started on this one. Don't give me the answer, though.
So I am trying to find the solution to this linear system through substitution. {  2x  y = 3 and y  12 = x.
Rachel98
 3 years ago
I need help getting started on this one. Don't give me the answer, though. So I am trying to find the solution to this linear system through substitution. {  2x  y = 3 and y  12 = x.

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UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1isolate y in the second equation , then substitute this into the first equation

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1actually it would be simpler to just substitute x from the second equation into the first ( as it is already isolated)

Rachel98
 3 years ago
Best ResponseYou've already chosen the best response.1Oh, so to substitute we get  2(y  12) = 3?

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1yeah that's the quickest way ,

Rachel98
 3 years ago
Best ResponseYou've already chosen the best response.1So, to solve I would distribute the 2. So I get  2y + 24 = 3, then I subtract 24 from both sides and get  2y =  21, I divide both sides by  2 and get y = 10.5? Is that right?

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1your working looks right , but there must be a mistake somewhere

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1ahh you forgot one term  2x  y = 3 , y  12 = x. 2(y12)y=3  2y + 24 y =3

Rachel98
 3 years ago
Best ResponseYou've already chosen the best response.1Since the variables are on the same side do you add them together and get  3y?

Rachel98
 3 years ago
Best ResponseYou've already chosen the best response.1Okay so we get  3y + 24 = 3 and then we subtract 24 from both sides and get  3y =  21, then we divide both sides by negative 3 and get y = 7

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1very good. now just use this to find x and your done

Rachel98
 3 years ago
Best ResponseYou've already chosen the best response.1So, we get  2x  7 = 3. So then we add 7 to both sides and get  2x = 10, then we divide both sides by  2 and get x =  5?

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1\[\LARGE\color{red}{\checkmark\checkmark}\]

Rachel98
 3 years ago
Best ResponseYou've already chosen the best response.1Thanks for the help. So the solution is ( 5, 7)?

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1i might have been quicker to substitute y=7 into the second equation but the result is the same (5,7) Yes!
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