Solutions for the linear system 3x+y=-15 and 2x-3y=23

3x + y = - 15 ... y = - 3x - 15 ... so sub in - 3x - 15 for y in the other equation

2x - 3y = 23

2x - 3 (-3x - 15) = 23

2x + 9x + 45 = 23

11x = 23 - 45

11x = - 22

x = - 22/11

x = - 2

y = - 3x - 15

y = - 3 (-2) - 15

y = 6 - 15

y = - 9

solution is (-2,-9)

Solve equation [1] for the variable y

[1] y = - 3x - 15

/ / Plug this in for variable y in equation [2]

[2] 2x - 3• (-3x-15) = 23 [2] 11x = - 22

/ / Solve equation [2] for the variable x

[2] 11x = - 22 [2] x = - 2

/ / By now we know this much:

x = - 2 y = - 3x-15

/ / Use the x value to solve for y

y = - 3 (-2) - 15 = - 9 Solution : {x, y} = {-2,-9}