1. Stating the problem: Solve the system of linear equations: $$-5 + 3x = 16$$ $$4x - 11 = -3$$ 2. Solve the first equation for $x$: Add 5 to both sides: $$-5 + 3x + 5 = 16 + 5$$ $$3x = 21$$ Divide both sides by 3: $$\cancel{3}x = \frac{21}{\cancel{3}}$$ $$x = 7$$ 3. Verify the solution in the second equation: Substitute $x = 7$: $$4(7) - 11 = -3$$ $$28 - 11 = -3$$ $$17 \neq -3$$ Since $x=7$ does not satisfy the second equation, solve the second equation separately: Add 11 to both sides: $$4x - 11 + 11 = -3 + 11$$ $$4x = 8$$ Divide both sides by 4: $$\cancel{4}x = \frac{8}{\cancel{4}}$$ $$x = 2$$ 4. Conclusion: The two equations give different values for $x$ ($7$ and $2$), so the system has no solution (the lines are parallel). Final answer: No solution (inconsistent system).