# Simultaneous equations elimination 2

19. Apr 2015
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### Simultaneous equations elimination 2

• 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.