The substitution method works by solving one of the equations for one of the variables, and then plugging back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

So first lets solve 'y+3x=-4' for 'y':

y = -3x - 4

Click here to see the solving for 'y'.

The, plug 'y = -3x - 4' into the second equation '2x-3y=21' and solve for 'x':

2x - 3*(-3x-4) = 21

........

Click here to see the solution for 'x'

........

x = 9/11

Plug 'x = 9/11' into 'y = -3x - 4'  to find 'y':

y = -3(9/11) - 4

........

Click here to see the step by step solution for 'y':

........

y = -71/11

y = - 6 5/11

The solution for the system of equations is:

x = 9/11

y = - 6 5/11