Can two equation have same solutions?

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If you are given two equations of degree one and two variables can they have same solution.

For example:

\begin{align} Ax+By+C&=0 \tag{1} \\ Sx+Ty+U&=0 \tag{2} \end{align}

Where: $A \ne S$, $T \ne B$, $C \ne U$.

Can it be possible if any two numbers $x$ and $y$ satisfy [1] then they also satisfy [2]. At first glance the answer seems to be "no", but if you think about your answer then you will come to realize that "no" is, not an answer but is, "intuition". And "intuition" can be wrong. If you are going to answer then please provide a proof of your answer.

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Yes, they can have.

Suppose the two equations be:

$$ a_0 x + b_0 y + c_0 = 0 $$

$$ a_1 x + b_1y + c_1 = 0 \tag{*}$$

For $a_0 = \lambda a_1; b_0 = \lambda b_1; c_0 = \lambda c_1$

We have equations like this:

$$ a_0x + b_0y + c_0 = 0 $$ $$ \lambda (a_0x + b_0y + c_0) = 0 \tag {*}$$

Now, they have the same solutions.