Question 81452
Step 1: Isolate one variable, using one of the equations
Step 2: Substitute that into the other equation to eliminate the variable
Step 3: Solve that resulting equation for the remaining variable
Step 4: Solve for the variable that was eliminated
Step 5: Check the solution

Step 1 will be easy here if we use the 2nd equation, {{{x+y=-9}}}, to isolate a variable.  It could easily be x or y.  Let's just do x since it doesn't matter that much.

{{{x = -9-y}}}

Step 2: Substitute that expression for x into the first equation
{{{3x - y = -7}}}
{{{x = -9-y}}}
{{{3 * (-9-y) - y = -7}}}

Step 3: Simplify and solve for y
{{{ -27 - 3y - y = -7}}}
{{{ -27 - 4y = -7 }}}
Add 27 to both sides
{{{ -4y = 20 }}}
Divide both sides by -4
{{{ y = -5 }}}

Step 4: Find x
{{{ x = -9 - y}}}
{{{ x = -9 - (-5) = -4 }}}

Step 5: Check the solution
{{{ x = -4}}}, {{{y = -5 }}}
{{{ 3*x - y = -7 }}}
{{{ x + y = -9 }}}
{{{ 3 * -4 - (-5) = -12 + 5 = -7 }}} YES 
{{{x + y = -4 + (-5) = -9 }}} YES 
The solution is correct