1. **State the problem:** We are given three equations: $$x = y + 40$$ $$x + y = 46$$ $$4x + 2y = 100$$ We need to find the values of $x$ and $y$ that satisfy these equations. 2. **Use substitution:** From the first equation, we have $x = y + 40$. We can substitute this into the second equation: $$ (y + 40) + y = 46 $$ 3. **Simplify the second equation:** $$ y + 40 + y = 46 $$ $$ 2y + 40 = 46 $$ 4. **Isolate $y$:** $$ 2y = 46 - 40 $$ $$ 2y = 6 $$ 5. **Divide both sides by 2:** $$ \cancel{2}y = \cancel{2}3 $$ $$ y = 3 $$ 6. **Find $x$ using the first equation:** $$ x = y + 40 = 3 + 40 = 43 $$ 7. **Check the solution in the third equation:** $$ 4x + 2y = 4(43) + 2(3) = 172 + 6 = 178 $$ Since $178 \neq 100$, the three equations are inconsistent and cannot all be true simultaneously. **Final answer:** The system of three equations is inconsistent; no single $(x,y)$ satisfies all three simultaneously.