Solve equation [2] for the variable y
<span> [2] y = 6x + 3z - 12
</span>
// Plug this in for variable y in equation [1]
<span><span> [1] 4x + 3•(6x+3z-12) - z = -6
</span><span> [1] 22x + 8z = 30
</span></span>
// Plug this in for variable y in equation [3]
<span><span> [3] 8x + 2•(6x+3z-12) + 4z = 6
</span><span> [3] 20x + 10z = 30
</span></span>
// Solve equation [3] for the variable z
<span> [3] 10z = -20x + 30
[3] z = -2x + 3</span>
// Plug this in for variable z in equation [1]
<span><span> [1] 22x + 8•(-2x+3) = 30
</span><span> [1] 6x = 6
</span></span>
// Solve equation [1] for the variable x
<span><span> [1] 6x = 6</span>
<span> [1] x = 1</span> </span>
// By now we know this much :
<span><span> x = 1</span>
<span> y = 6x+3z-12</span>
<span> z = -2x+3</span></span>
<span>// Use the x value to solve for z
</span>
<span> z = -2(1)+3 = 1 </span>
<span>// Use the x and z values to solve for y
</span><span><span> y = </span>6(1)+3(1)-12 = -3 </span>
Solution :<span><span> {x,y,z} = {
1,-3,1}</span> </span>
