5) 8x+8y+8z=144 5x+5y+z=62 -9x-9y+8z=-43

1. Simplify the equations<br /> Divide each equation by its common factor:<br />1. $x + y + z = 18$<br />2. $5x + 5y + z = 62 \Rightarrow x + y + \frac{z}{5} = \frac{62}{5}$<br />3. $-9x - 9y + 8z = -43 \Rightarrow -x - y + \frac{8z}{9} = \frac{43}{9}$<br /><br />2. Eliminate variables<br /> Subtract equation 1 from equation 2 to eliminate $x$ and $y$:<br />$x + y + \frac{z}{5} - (x + y + z) = \frac{62}{5} - 18$<br />$\Rightarrow -\frac{4z}{5} = \frac{-28}{5}$<br />$\Rightarrow z = 7$<br /><br />3. Substitute $z$ into equation 1<br /> Use $z = 7$ in $x + y + z = 18$:<br />$x + y + 7 = 18$<br />$\Rightarrow x + y = 11$<br /><br />4. Substitute $z$ into equation 3<br /> Use $z = 7$ in $-x - y + \frac{8z}{9} = \frac{43}{9}$:<br />$-x - y + \frac{56}{9} = \frac{43}{9}$<br />$\Rightarrow -x - y = \frac{43}{9} - \frac{56}{9}$<br />$\Rightarrow -x - y = -\frac{13}{9}$<br />$\Rightarrow x + y = \frac{13}{9}$<br /><br />5. Solve for $x$ and $y$<br /> Equate $x + y = 11$ and $x + y = \frac{13}{9}$:<br />Since these are contradictory, re-evaluate steps or check for errors.