> Solving simultaneous equation by elimination
Solving simultaneous equation by elimination
This method for solving simultaneous equations involves adding together the equations or subtracting one equation from another to eliminate a variable.
If the variable in both equations has the same coefficient but be opposite in sign, simply add the equations together to remove the variable.
If the variable in both equations has the same coefficient and same sign, simply subtract one equation from another to remove the variable.
If the variable in both equations do not have the same coefficient, before adding together the equations or subtracting one equation from another, one or both of the equations must be multiplied by a number so that in the resulting simultaneous equations one variable has the same coefficient in both equations.
Example 1
Solve the following simultaneous equations
3x + 2y = 4
5x - 2y = 12
Solution:
Adding the two equations together, we have
3x + 2y + 5x - 2y = 4 + 12
8x = 16
combining like terms
x = 2
dividing both sides by 8
Substituting 2 for x in the first equation 3x + 2y = 4, we have
3(2) + 2y = 4
6 + 2y = 4
2y = -2
subtracting 6 from both sides
y = -1
dividing both sides by 2
So the solution is
x = 2
y = -1
Example 2
Solve the following simultaneous equations
2x + 3y = 5 (1)
x + 2y = 3 (2)
Solutions
As either variable does not have same coefficient in both equations, one or both
of the equations must be multiplied by a number so that in the resulting
simultaneous equations one variable has the same coefficient in both equations.
In this case, we need only to multiply the second equation by 2. The resulting
simultaneous equation is as follows:
2x + 3y = 5 (3)
2x + 4y = 6 (4)
Subtracting the first equation from the second one, we have
2x + 4y - (2x + 3y) = 6 - 5
2x + 4y - 2x - 3y =1
removing the parentheses
y = 1
combining like terms
Substituting 1 for y in equation (2), we have
x + 2(1) = 3
x + 2 = 3
x = 1
So the solution is
x = 1
y = 1