11x +2y = -1
2x +3y = 13 Found 2 solutions by whenindoubt, AnlytcPhil:Answer by whenindoubt(13) (Show Source):
You can put this solution on YOUR website! this is a multi variable linear equation. the best method is to find a way to elminate one of the variables
-3 (11x + 2y = -1 )
by distributing this -3 we can eliminate the y varible. this does not change the equation because we are distributing evenly by the same scalar. the new equation would be
-33x -6y = 3
now take
2 (2x + 3y = 13)
for the same purposes, the new equation would be
4x + 6y = 26
and now adding the two new equations together the y variable cancels and we get.
-29x=29
x= -1
then by placing x into either equation we get the y variable.
Solve by the addition method:
11x + 2y = -1
2x + 3y = 13
To eliminate the x's, we multiply thru each equation by numbers that will
cause the new coefficients of x to become equal in absolute value but
opposite in sign.
The least common multiple of coefficients of x, 11 and 2, is 22. Thus we
want to cause one of the coefficients of x to become +22 and the other -22.
To accomplish this we multiply the first equation thru by 2 and the second
equation by -11
22x + 4y = -2
-22x - 33y = -143
-----------------
Adding these vertically:
-29y = -145
y = 5
------------------------
11x + 2y = -1
2x + 3y = 13
The least common multiple of coefficients of y, 2 and 3, is 6. Thus we
want to cause one of the coefficients of x to become +6 and the other -6.
To accomplish this we multiply the first equation thru by 3 and the second
equation by -2
33x + 6y = -3
-4x - 6y = -26
-----------------
Adding these vertically:
29x = -29
x = -1
So the solution is (-1,5)
Edwin
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