1. We are given the system of equations: $$2+3x=-7$$ $$2x+9=-2x+1$$ $$1-5x=2+4x$$ 2. Let's solve the first equation for $x$: $$2+3x=-7$$ Subtract 2 from both sides: $$\cancel{2}+3x=\cancel{-7}-2$$ $$3x=-9$$ Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}}=\frac{-9}{3}$$ $$x=-3$$ 3. Now solve the second equation for $x$: $$2x+9=-2x+1$$ Add $2x$ to both sides: $$2x+2x+9=1$$ $$4x+9=1$$ Subtract 9 from both sides: $$4x+\cancel{9}=1-9$$ $$4x=-8$$ Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}}=\frac{-8}{4}$$ $$x=-2$$ 4. Finally, solve the third equation for $x$: $$1-5x=2+4x$$ Subtract 2 from both sides: $$1-2-5x=\cancel{2}-2+4x$$ $$-1-5x=4x$$ Add $5x$ to both sides: $$-1-5x+5x=4x+5x$$ $$-1=9x$$ Divide both sides by 9: $$\frac{-1}{9}=\frac{9x}{9}$$ $$x=-\frac{1}{9}$$ 5. Summary of solutions: - For equation 1: $x=-3$ - For equation 2: $x=-2$ - For equation 3: $x=-\frac{1}{9}$ Each equation has a different solution for $x$.