Solution:
Given:
[tex]\begin{gathered} 4x-5y=2 \\ 3x-y=8 \end{gathered}[/tex]Two systems of equations are equivalent if they have exactly the same solution set.
Hence, we determine the solution to the system of equations.
[tex]\begin{gathered} 4x-5y=2\ldots\ldots.\ldots.\ldots.\ldots.(1) \\ 3x-y=8\ldots\ldots.\ldots\ldots\ldots\ldots..(2) \\ \\ m\text{ ultiplying equation (2) by 5} \\ 5(3x-y)=5(8) \\ 15x-5y=40 \\ \\ \text{Solving both equations (1) and the newly formed equation (2) simultaneously,} \\ 4x-5y=2\ldots\ldots\ldots\ldots(1) \\ 15x-5y=40\ldots\ldots\ldots.\mathrm{}(2) \end{gathered}[/tex]
Subtracting equation (1) from equation (2),
Equation (2) - equation (1) becomes;
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