This document describes the elimination method for solving simultaneous linear equations. It involves labeling the equations, subtracting one equation from the other to eliminate a variable with equal coefficients of the same sign, solving for the eliminated variable, and then substituting back into one of the original equations to solve for the remaining variable. As an example, it shows using this method to solve the equations 2x + y = 3 and 4x + y = 11, obtaining solutions of x = 4 and y = -5.

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

2. Equal coefficients and opposite in
sign
Given two equations: 2x + y = 3
 4x + y =11
Note that the coefficients are equal and same sign for
y.

3. Label Equations
Let 2x + y = 3 be equation 1
 4x +y = 11 be equation 2
Subtract equation 2 from 1 to eliminate the variable
with like coefficient and same sign.

4. Add both equations
 2x + y = 3 eq 1
 - (4x + y = 11) eq 2
2x-4x +y-y = 3-11
 -2x = -8
 -2x
/-2= -8
/-2
Having solve for x=4 solve for y in either equation 1 or
2.

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

6. Prove
2x + y = 3 and 4x+ y = 11 when x=4 and y=-5
2(4)+(-5)= 3 and 4(4)+(-5)=11 substitute
 8 - 5 = 3 and 16 - 5= 11
 3 = 3 and 11 = 11 so it hold to be true.

7. Conclusion
Label both equations (Example eq 1 and eq 2).
Coefficient are equal and same for a given variable.
Subtract one equation from the other to eliminate the
said variable.
Substitute for the solved variable and solve for the
eliminated variable.