when you want to solve an elimination question
3x -2y = 11. ( equation 1)
-3x - y = 6. ( equation 2)
To proceed in the solution, we have to make one of the variable' s coefficient equal on both equation.
I want to make the coefficient of variable X equal on both equation and to do this , the coefficient of X in equation 1 will be used to multiply the whole of equation 2 .while the coefficient of X in equation 2 will be used to multiply the whole of equation 1.
(-3) 3X - 2y = 11 ( equation 1)
(3) -3X - y = 6 ( equation 2)
-9X +6y = -33 ( equation 1)
- 9x - 3y = 18 ( equation 2)
( now , we have to eliminate X and inorder to do that , we substrate equation 1 from 2)
-9X -(-9X) ,+6y -(-3y) ,-33-18
-9X +9x , +6y +3y , -51
9 y = -51
y = -51/9
y = -5⅔
Substitute y = -5⅔ in equation 1
3x -2(-5⅔) = 11
3X - 2 ( -17/3) = 11
3X + 34/3 =11
divide through by the LCM which is 3
3( 3x) + 3 ( 34 /3 ) = 3*11
9x +34 = 33
9x = 33-34
9x = -1
X= -1/9
therefore, y = -5⅔ , X = -1/9
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