How do you solve, 3x-11y=9; -9x-33y=18. If there is no solution, why?
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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:
For a detailed explanation on how to use them, you can visit:
Source(s):This same question.
multiply the first equation by 3 so you get
So the two equations look like this:
Add those to up, then you'll get
Add the y in one of those equations let say number 2:
3x - 11y = 9 (1)
-9x - 33y = 18 (2)
(1) <=> 9x - 33y = 18
(1) # (2) => vô nghiệm
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
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.