Question

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

Answer 1

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} 

Answer 2

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)