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.