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# Need help with system of Equations

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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.

Mar 12, 2019

#1
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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 !

Mar 12, 2019
#2
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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.

Mar 12, 2019