3. Create a system of equations that has no solutions. Then prove that it has no solutions algebraically.
4. Create a system of equations that has infinite solutions. Then prove that it has no solutions algebraically.
+37159 y= 1/2 x +14
2y-x = 44 Hint: these are equations of lines that do not cross....so no solution set
take it away !
+9673 3. \(\begin{cases} 2x + y= 1\\2x+y = 5\end{cases}\)
Substituting equation 1 into equation 2, we get 5 = 1, which means no solution.
4. \(\begin{cases}2x + y = 1\\4x+2y = 2\end{cases}\)
Substituting equation 1 into equation 2, we get 2 = 2 which is always true. Therefore, any pair of (x, y) satisfies this equation and thus it has infinite solutions.
