3u - 2v = 12
7u + 2v=8
using elimination by addition
Graphing these.
7u + 2v=8
using elimination by addition
Graphing these.
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add the two functions
10u + (-2v + 2v) = 20
The 2v cancels out and you're left with
10u = 20
Divide by ten u = 2
Plug 2 back into either of the original equations and solve for v. Let's do the second one, simply because addition is preferable to subtraction.
7(2) + 2v = 8
subtract both sides by 14 and get 2v = -6
v = -3.
Set those points along an x,y coordinate plan and graph. Easy
10u + (-2v + 2v) = 20
The 2v cancels out and you're left with
10u = 20
Divide by ten u = 2
Plug 2 back into either of the original equations and solve for v. Let's do the second one, simply because addition is preferable to subtraction.
7(2) + 2v = 8
subtract both sides by 14 and get 2v = -6
v = -3.
Set those points along an x,y coordinate plan and graph. Easy
-
Elimination method means you want to take out one of the variables ('u' and 'v' are variables)
So first we need to make the variables equal amounts. So if we have 7u, then we need to change 3u into 7u. HOWEVER, we already have 2v and -2v so we can use this instead
Next we want to subtract the equal amounts so we get rid of that variable. Luckily, we can just add 2v and -2v together to make them 0
3u - 2v = 12
7u + 2v = 8
+ ------------------
10u + 0 = 20
The final steps are figuring out what v and u are in terms of numbers
So we divide 20 by 10:
10u / 10 = 20 / 10
u = 2
And then for v we insert 2 into 'u':
3u - 2v = 12
3(2) - 2v = 12
-2v = 12-6
-2v = 6
v = -3
So first we need to make the variables equal amounts. So if we have 7u, then we need to change 3u into 7u. HOWEVER, we already have 2v and -2v so we can use this instead
Next we want to subtract the equal amounts so we get rid of that variable. Luckily, we can just add 2v and -2v together to make them 0
3u - 2v = 12
7u + 2v = 8
+ ------------------
10u + 0 = 20
The final steps are figuring out what v and u are in terms of numbers
So we divide 20 by 10:
10u / 10 = 20 / 10
u = 2
And then for v we insert 2 into 'u':
3u - 2v = 12
3(2) - 2v = 12
-2v = 12-6
-2v = 6
v = -3
-
if all of them use the elimination
3u - 2v = 12
7u + 2v=8
----------------- + elimination v
10u + 0 = 20
10u = 20
u = 20/10
u = 2
21u - 14v = 84 ← after multiplied by 7
21u + 6v = 24 ← after multiplied by 3
----------------------- -
…..-20v = 60
v = 60/-20
v = -3
3u - 2v = 12
7u + 2v=8
----------------- + elimination v
10u + 0 = 20
10u = 20
u = 20/10
u = 2
21u - 14v = 84 ← after multiplied by 7
21u + 6v = 24 ← after multiplied by 3
----------------------- -
…..-20v = 60
v = 60/-20
v = -3