By Team Aakash Byju's | 15th December 2022
Multiply both of the given equations by non-zero constants to make the coefficients of any of the variables (x or y) numerically equal.
Add or subtract one equation from the other such that one variable is eliminated. If you receive an equation with only one variable, proceed to Step 3. Else,
-21x + 3y = 6
3x - 3y = 3
+
Eliminate
(in this case , add)
-18x + 0y = 9
(Continues)
If we get a true statement with no variables, then the original pair of equations has an endless number of solutions.
2y = 6-4x
2(-2x + 3) = 6-4x
-4x + 6 = 6-4x
adding 4x on both sides
4x-4x + 6 = 6-4x+4x
6 = 6
(y = -2x+3)
. .
.
(Continues)
If we get a false statement with no variables, the original pair of equations has no solution, i.e., it is inconsistent.
2x + 2y = 18
-2x - 2y = -6
+
0 = 12
To find the value of one variable (x or y), solve the equation.
2x - (24 - x) = -6
2x - 24 + x = -6
3x - 24 = -6
x = 6
3x = 18
Use this value to solve any of the given equations to find the value of another variable.
x = 6
y = 24 - x
y = 24 - 6
y = 18
For example: Consider equations,
2x + 7y = 10…………….. (1)
3x + y = 6…………….. (2)
multiplying equation (1) by 3 and equation (2) by 2, we get,
6x + 21y = 30……………..(3)
6x + 2y = 12……………….(4)
Subtracting equation (4) from equation (3). We get,
6x + 21y – 6x – 2y = 30 – 12
⇒ 19y = 18
y =
18
19
To get the value of x, substitute the value of y in equation (2),
3x + = 6
⇒ 3x = 6-
=> x =
96
19
18
19
18
19
3x =
96
57
32
19
=> x =