The document describes the elimination method for solving simultaneous linear equations. It involves: 1) Identifying equations where one variable has equal and opposite coefficients; 2) Adding the equations to eliminate this variable; 3) Solving the resulting equation for the remaining variable; and 4) Substituting back into one of the original equations to solve for the eliminated variable. As an example, it shows using this method to solve the equations 4x + y = 11 and 3x - y = 3 for x = 2 and y = 3.

1. Solve simultaneous linear equations by Elimination
Method
By Hector Castellanos

2. Equal coefficients and opposite in
sign
Given two equations: 4x + y = 11
 3x – y = 3
Note that the coefficients are equal and opposite in
sign so the sum of these two would be 0. Eg. +1-1=0 for
the variable y in this example.

3. Label Equations
Let 4x + y = 11 be equation 1
 3x – y = 3 be equation 2
Add both equations to eliminate the variable y with
equal coefficient and opposite in sign to solve for the
other variable.

4. Add both equations
 4x + y = 11 eq 1
 + (3x – y = 3) eq 2
4x+3x +y-y = 11+3
 7x = 14
 7x
/7 = 14
/7 ÷ both side by 7 (coefficient)
 x = 2
Having solve for x=2, solve for y in either equation 1
or 2.

5. Solve for the second variable
Solve for y when x=2 by substitution in eq 1.
 4x + y = 11
4 (2) + y = 11 substitute for x
 8 + y = 11
 8-8 + y = 11-8 subtract 8 to both sides
 y = 3
Therefore when x=2,y=3 in the given equations.

6. Prove
4x + y = 11 and 3x- y = 3 when x=2 and y=3
4(2)+3= 11 and 3(2)-3=3 substitute
 8 + 3= 11 and 6 - 3= 3
 11=11 and 3=3 so it hold to be true.

7. Conclusion
Label both equations (Example eq 1 and eq 2).
Coefficients are equal and opposite in sign for a given
variable.
Add both equations to eliminate the variable.
Solve for variable and then substitute for the second
variable.