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# How do you solve, 3x-11y=9; -9x-33y=18. If there is no solution, why?

Member since:
December 22, 2007
Total points:
12,974 (Level 6)

## Best Answer - Chosen by Voters

The first equation is 3x-11y=9 and the second equation is;

3x+11y=-6 (you divide the equation by -3)

so

3x-11y=9
3x+11y=-6

6x=3
x=1/2

and 3/2-11y=9 3/2-9=11y y=-0.6816
100% 1 Vote

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• by Peter
Member since:
February 23, 2010
Total points:
788 (Level 2)
The second equation is NOT a multiple of the first one. If instead of an 18 there was a 27, ok, but that is not the case.
And there are not infinite multiple solutions, just one, as outlined in marckd2002's answer which is correct. There are different ways to get to it, but I find this method to be the simplest.
This is called the substitution method.
The method of substitution involves five steps:

Step 1: Solve for y in equation (1).
Step 2: Substitute this value for y in equation (2). This will change equation (2) to an equation with just one variable, x.
Step 3: Solve for x in the translated equation (2).
Step 4: Substitute this value of x in the y equation you obtained in Step 1.
Step 5: Check your answers by substituting the values of x and y in each of the original equations. If, after the substitution, the left side of the equation equals the right side of the equation, you know that your answers are correct.

There are other methods you can use, they are:

Elimination,
Matrices,
Graphing.

For a detailed explanation on how to use them, you can visit:
http://www.sosmath.com/soe/SE2001/SE2001…

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• Member since:
June 25, 2007
Total points:
2,474 (Level 3)
You need to take a facto away

3x - 11y = 9
3x = 11y + 9
x = (11y + 9) / 3

then you substitute the x in the other variable

-9(11y + 9)/3 -33y = 18
-33y - 27 -33y = 18
-66y = 18 + 27
y = -15/22

and then change y for the number

3x -11 (-15/22) = 9
3x +15/2 = 9
3x = 3/2
x= 1/2
• by D.W.
Member since:
April 20, 2007
Total points:
197,116 (Level 7)
The second equation is a multiple of the first. Since you don't have two independent equations, you can't find a unique solution. There are infinitely many solutions.
• by Ozz123
Member since:
February 26, 2009
Total points:
2,114 (Level 3)
3x-11y=9
-9x-33y= 18

multiply the first equation by 3 so you get
9x-33y=27

So the two equations look like this:
9x-33y=27
-9x-33y= 18
Add those to up, then you'll get
-66y=45
y= -15/22

Add the y in one of those equations let say number 2:
-9x-(33*-15/22)=18
-9x+22.5=18
-9x=-4.5
x=0.5
• by _TIM_
Member since:
November 15, 2009
Total points:
1,069 (Level 3)
{
3x - 11y = 9 (1)
-9x - 33y = 18 (2)

(1) <=> 9x - 33y = 18

(1) # (2) => vô nghiệm