Linear Equations In Two Variable

[rajivsharma0723]

Solve the following system of equations using the elimination method by equating coefficients;

11x - 5y + 61 = 0
3x - 20y - 2 = 0

[mathpedia]

Solve the following system of equations using the elimination method by equating coefficients;

11x - 5y + 61 = 0
3x - 20y - 2 = 0

First of all we separate the variables' coefficients from the constants:

11x - 5y = -61 (1)
3x - 20y = 2 (2)

The main idea of solving math system of equations with this method is to find each time the least common factor between all of the coefficients found on a specific column. (is about the column you want to eliminate )

For example, for the x variable, we have the column formed with 11 and 3. For y variable, the column is made with the numbers -5 and -20. And finally, for the constants, we have -61 and 2.

So if you need to reduce x, you just need to find the least common factor between 11 and 3, and then you divide it to 11, respective to 3, and next, you just multyple both equations with those two results. After that, is simple. All you need is reducing (2) from (1) or viceversa.

Assume you want to reduce x. The least common factor between 11 and 3 is 33. Dividing 33 by 11 you get 3, and by 3, it' s 11:

(1) <=> 3(11x - 5y) = 3*(-61) <=> 33x - 15y = -183 (3)
(2) <=> 11(3x-2y) = 11*2 <=>33x - 22y = 22 (4)

Reducing (3) with (4) we get (33x - 33x) + (-15y) - (-22y) = -183 - 22 <=> 7y = -161 => y = (-161) / 7 => y = 23. So when reducing on columns, you first made the substractions on each column (including the result column) and then you just add the substractions on the variables' columns and equal them to the substraction from the result column.

With y=7 we just go to (2):
3x - 20*2 = 2 => 3x - 40 = 2 => 3x = 42 => x = 42/3 => x=14.

[amit28it]

Solve the following system of equations using the elimination method by equating coefficients;

11x - 5y + 61 = 0
3x - 20y - 2 = 0

The equation
11x - 5y + 61 = 0
3x - 20y - 2 = 0
step by step .
Firstly we will eliminate one variable :-

Multiply eq--2 by 11 and eq 2 by 3:-

33x - 15y =-183
-33x +220y =- 22
By adding two equations we get
205 y = -205
y = -1
so now you can find x.