Solution :<span><span> {x,y,z} = {-3,-2,-1}</span>
</span>System of Linear Equations entered :<span><span> [1] x + 6y + 3z = -18
</span><span> [2] -x + 6y - 3z = -6
</span><span> [3] 5x - 6y + 3z = -6
</span></span>Solve by Substitution :
// Solve equation [1] for the variable x
<span> [1] x = -6y - 3z - 18
</span>
// Plug this in for variable x in equation [2]
<span><span> [2] -(-6y-3z-18) + 6y - 3z = -6
</span><span> [2] 12y = -24
</span></span>
// Plug this in for variable x in equation [3]
<span><span> [3] 5•(-6y-3z-18) - 6y + 3z = -6
</span><span> [3] - 36y - 12z = 84
</span></span>
// Solve equation [2] for the variable y
<span><span> [2] 12y = - 24</span>
<span> [2] y = - 2</span> </span>
// Plug this in for variable y in equation [3]
<span><span> [3] - 36•(-2) - 12z = 84
</span><span> [3] - 12z = 12
</span></span>
// Solve equation [3] for the variable z
<span><span> [3] 12z = - 12</span>
<span> [3] z = - 1</span> </span>
// By now we know this much :
<span><span> x = -6y-3z-18</span>
<span> y = -2</span>
<span> z = -1</span></span>
<span>// Use the y and z values to solve for x
</span><span><span> x = </span>-6(-2)-3(-1)-18 = -3 </span>
Solution :<span><span> {x,y,z} = {-3,-2,-1}</span>
Processing ends successfully </span>
