Consider the system x2y 2 2x3y 7 To eliminate x multiply

Consider the system x+2y = - 2 2x+3y = - 7 To eliminate x, multiply the first equation by and the second by Resulting system of equations: Adding the two equations above gives: Solving for y gives y = Once you know the value of y, you could obtain x by substituting this value in one of the original equations, for the sake of practice, we are going to eliminate y starting again with the original system: x+2y = - 2 2x+3y= - 7 To eliminate y, multiply the first equation by and the second by Resulting system of equations: Adding the two equations above gives: Solving for x gives x =

Solution

x +2y = -2 ---(1)

2x +3y = -7 ---(2)

Multiply equation (1) by 2

Multiply equation (1) by -1

Resulting : 2x + 4y = -4

-2x -3y = 7

Adding the above two equations: y = 3

x= -2 -2y = -2 -6 = -8

2) to eliminate y multiply 1st equation by -3 and 2nd equation by 2

-3x - 6y = 6

4x + 6y = -14

---------------------- ( adding the two equations )

x = - 8 ( solving for x )