If the linear equations x_1 + Kx_2 = c and x_1 + Tx_2 = d have the same solution set, equations are indentical

How can this be proved? If both equations have the same solution set, how are the equations identical?

If the linear equations x_1 + Kx_2 = c and x_1 + Tx_2 = d have the same solution set, equations are indentical
Let K = 10 and c = 30


Then x1 +10x2 = 30


x1 = 10 and x2 = 2 are one possible solution.





Let T = 20 and d = 42


Then x1 +20x2 = 42


x1 =10 and x2 =2 are also a solution of this equation





So we have two different equations with the same solution set. Your conjecture is false as i have proven by counterexample.

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