3-Elimination+method

Elimination Method

__Examples:__ -4 ( 3x-2y=6 ) 5 The numbers in pink show one equation and the numbers in blue show another. 3 ( 4x+5y=-2 ) 2 1) First you check to see if the variables have opposite integers. -12x+8y=-24 2) The you mulptiply each equation by its opposite to make the numbers opposite. + __12x+15y=-6__ 3) Then you add the equations. The opposite integers cancel out.   __23y=-30__ 4) Then you divide both sides by the left over variables coefficient. That gives you, your y.  23 23   y=-30/23 15x-10y=30 1) On this equation you use the other variables to cancel out the ones you used last time to get x. +8x+10y=-4 2) Then you add the equations. 23x=26 3) The divide the variables coefficient to get your x. 23 23  x=26/23

Another example: 3 (-4x-5y=-1) 2 1) First you take the equation and make the variables coefficients opposite.     -5 (2x-3y=8) 4      -8x -10y=-2 -12x-15y=-3 2) Then you add the equations and divide the variables coefficient, that is what gives you your x and y.    __8x – 12y=32 -10x=15y=-40__ __ -22y=-30 -22x=-43 __ -22 -22   Y=-30/22 x=43/22 (43/22, -15/11)