Solving a Linear equation with substitution or elimination
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Re: Solving a Linear equation with substitution or eliminati
You have these two equations:
-3x + y = 11
x + 3y = 9
Since your subject line suggests that you can either use substitution OR elimination, I'll show you how you can use "substitution."
You can solve the first equation for y....ADD 3x to both sides:
-3x + y = 11
-3x + y + 3x = 11 + 3x
y = 11 + 3x
Ok....now, you know that y = 11 + 3x. So, you can substitute (11 + 3x) for "y" in the second equation:
x + 3y = 9
x + 3(11 + 3x) = 9
x + 33 + 9x = 9
10x + 33 = 9
10x + 33 - 33 = 9 - 33
10x = -24
(10x) / 10 = (-24) / 10
x = -12/5
y = 11 + 3x
y = 11 + 3(-12/5)
y = 11 + (-36/5)
y = (55/5) + (-36/5)
y = 19/5
Check....are both original equations true when x = -12/5 and y = 19/5?
-3x + y = 11
-3(-12/5) + (19/5) = 11
36/5 + 19/5 = 11
55/5 = 11
11 = 11
Ok...that one checks.
x + 3y = 9
(-12/5) + 3(19/5) = 9
(-12/5) + (57/5) = 9
(45/5) = 9
9 = 9
And that one checks, too.
polish said:
You have these two equations:
-3x + y = 11
x + 3y = 9
Since your subject line suggests that you can either use substitution OR elimination, I'll show you how you can use "substitution."
You can solve the first equation for y....ADD 3x to both sides:
-3x + y = 11
-3x + y + 3x = 11 + 3x
y = 11 + 3x
Ok....now, you know that y = 11 + 3x. So, you can substitute (11 + 3x) for "y" in the second equation:
x + 3y = 9
x + 3(11 + 3x) = 9
x + 33 + 9x = 9
10x + 33 = 9
10x + 33 - 33 = 9 - 33
10x = -24
(10x) / 10 = (-24) / 10
x = -12/5
y = 11 + 3x
y = 11 + 3(-12/5)
y = 11 + (-36/5)
y = (55/5) + (-36/5)
y = 19/5
Check....are both original equations true when x = -12/5 and y = 19/5?
-3x + y = 11
-3(-12/5) + (19/5) = 11
36/5 + 19/5 = 11
55/5 = 11
11 = 11
Ok...that one checks.
x + 3y = 9
(-12/5) + 3(19/5) = 9
(-12/5) + (57/5) = 9
(45/5) = 9
9 = 9
And that one checks, too.
Here's what galactus was telling you:
Your 2 equations:
-3x + y = 11 [1]
x + 3y = 9 [2]
3x + 9y = 27 [2] : multiply [2] by 3
-3x + y = 11 [1] : [1] remains same
============
0 + 10y = 38 : add the 2 equations together
10y = 38
5y = 19
y = 19/5 : kapish?
Your 2 equations:
-3x + y = 11 [1]
x + 3y = 9 [2]
3x + 9y = 27 [2] : multiply [2] by 3
-3x + y = 11 [1] : [1] remains same
============
0 + 10y = 38 : add the 2 equations together
10y = 38
5y = 19
y = 19/5 : kapish?
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Gracious! This should have been covered in the textbook and in class! :shock:polish said:
To make up for the missing lesson material, please study from some of the many great lessons available online:
. . . . .http://www.google.com/search?hl=en&...lts for "system linear equations solving"[/b]
Once you have studied some lessons (at least two!), the hints and steps the tutors gave you will make a whole lot more sense! :wink:
Eliz.