use additional method
3x = 4y + 1
4x + 3y = 1
need help figuring out what x and y is. if anyone can explain it to me that would be great. thanks.
3x = 4y + 1
4x + 3y = 1
need help figuring out what x and y is. if anyone can explain it to me that would be great. thanks.
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Additional method is really really easy. It's basically adding two formulas to eliminate extra variables so you can figure out what the variables actually represent.
1. The first step here would be to isolate all of the variable to one side.
3x - 4y = 1
4x + 3y = 1
What I did there was just subtract "4y" from each side of the first equation.
2. Now, the whole point of the additional method is to eliminate extra variables. It doesn't matter if you choose "x" or "y", which ever one is easier for you. So let's choose "y", because I don't like "y".
9x - 12y = 3
16x + 12y = 4
What I did here was make the constant in front of the "y" opposite of each other so in the end when you add these two together (12y-12y), the result is 0. Tada! you eliminated a variable. And to make the constants equal, I just multiplied all of the first equation by 3 and all of the second equation by 4 (To make the constant infront of the "y" the opposite value).
3. And now you're ready for the adding phase. Simply put these two equations into adding form like below:
__9x- 12y=3
+ 16x+12y=4 <-- And just add all of the corresponding terms! :D
-------------------------
25x + 0 = 7
25x= 7
x= 7/25
All I did there was line up the matching variable and constants (x to x, y to y, numbers to numbers). And since we already made the "y"'s cancel each other, we only had "x" left to figure out, which left you with simple algebra to figure out the answer.
4. Now, since you have the value for "x" you just need to plug it into whichever formula you want to plug it into:
3x = 4y + 1 (Plug the value for "x" in)
3(7/25) = 4y + 1
4y = (21/25) - 1
4y = -4/25
y = -1/25
5. And tada, you have just figured out both the values for "x" and "y".
x=7/25
y= -1/25
1. The first step here would be to isolate all of the variable to one side.
3x - 4y = 1
4x + 3y = 1
What I did there was just subtract "4y" from each side of the first equation.
2. Now, the whole point of the additional method is to eliminate extra variables. It doesn't matter if you choose "x" or "y", which ever one is easier for you. So let's choose "y", because I don't like "y".
9x - 12y = 3
16x + 12y = 4
What I did here was make the constant in front of the "y" opposite of each other so in the end when you add these two together (12y-12y), the result is 0. Tada! you eliminated a variable. And to make the constants equal, I just multiplied all of the first equation by 3 and all of the second equation by 4 (To make the constant infront of the "y" the opposite value).
3. And now you're ready for the adding phase. Simply put these two equations into adding form like below:
__9x- 12y=3
+ 16x+12y=4 <-- And just add all of the corresponding terms! :D
-------------------------
25x + 0 = 7
25x= 7
x= 7/25
All I did there was line up the matching variable and constants (x to x, y to y, numbers to numbers). And since we already made the "y"'s cancel each other, we only had "x" left to figure out, which left you with simple algebra to figure out the answer.
4. Now, since you have the value for "x" you just need to plug it into whichever formula you want to plug it into:
3x = 4y + 1 (Plug the value for "x" in)
3(7/25) = 4y + 1
4y = (21/25) - 1
4y = -4/25
y = -1/25
5. And tada, you have just figured out both the values for "x" and "y".
x=7/25
y= -1/25
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let
3x-4y=1 &__________ (i)
4x+3y=1___________(ii)
__________
we need to change now
1. multiplying eqn 1 by 4 & 2 by 3
then we can get in the from
and changing sign of eq 2
12x-16y=4
-12x-9y=-3
___________
-25y=1
so, y=-1/25
which is the required answer
3x-4y=1 &__________ (i)
4x+3y=1___________(ii)
__________
we need to change now
1. multiplying eqn 1 by 4 & 2 by 3
then we can get in the from
and changing sign of eq 2
12x-16y=4
-12x-9y=-3
___________
-25y=1
so, y=-1/25
which is the required answer