(2) ) -u+v-w=0 u-2w-3=0 -5w=1

To solve the system of equations, we can use the method of substitution or elimination. Let's solve it using the elimination method.<br /><br />First, let's isolate one variable in one of the equations. We can start with the third equation:<br /><br />$-5w = 1$<br /><br />Dividing both sides by -5, we get:<br /><br />$w = -\frac{1}{5}$<br /><br />Now, substitute this value of $w$ into the other two equations:<br /><br />$-u + v - (-\frac{1}{5}) = 0$<br /><br />$u - 2(-\frac{1}{5}) - 3 = 0$<br /><br />Simplifying these equations, we have:<br /><br />$-u + v + \frac{1}{5} = 0$<br /><br />$u + \frac{2}{5} - 3 = 0$<br /><br />Now, let's solve the first equation for $v$:<br /><br />$v = u - \frac{1}{5}$<br /><br />Substituting this value of $v$ into the second equation, we have:<br /><br />$u + \frac{2}{5} - 3 = 0$<br /><br />Simplifying further, we get:<br /><br />$u - \frac{13}{5} = 0$<br /><br />Adding $\frac{13}{5}$ to both sides, we have:<br /><br />$u = \frac{13}{5}$<br /><br />Now, substitute this value of $u$ back into the equation for $v$:<br /><br />$v = \frac{13}{5} - \frac{1}{5}$<br /><br />Simplifying, we get:<br /><br />$v = \frac{12}{5}$<br /><br />Therefore, the solution to the system of equations is:<br /><br />$u = \frac{13}{5}$, $v = \frac{12}{5}$, $w = -\frac{1}{5}$