how do i do elimination 8x + 6y =9 5x - 6y = 3

Question

8x + 6y =9

5x - 6y = 3

Answer 1

When you have two equations and two unknowns you can manipulate one equation so that it is either x= or y=. and substitute this expression into the other equation. But since these two equations have a 6y and -6y terms add the two equations. 

 

8x+6y=9

5x-6y=3

 

13x=12

x=12/13

 

Substitute this into either of the equations

5(12/13)-6y=3

[5(12)-3(13)]/13=6y

21/(13•6)=y

7/26=y

 

Or

8(12/13)+6y=9

6y=9-8(12/13)

6y=[9•13-8•12]/13

y=21/(13•6)=7/26

 

Check

8x+6y=9
5x-6y=3

 

 

8(12/13)+6(7/26)=9

 

multiply by 26

 

8(12)2+6(7)=9(26)

192+42=234 checks!

 

And check the other equation 
5(12/13)-6(7/26)=3

5(12)(2)-6(7)=3(26)

120-42=78

checks!