below have a solution? Explain. \[ \begin{array}{l}\frac{3}{4} x-3=y \\ 4 x-3 y=5\end{array} \]
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To determine if the equations have a solution, we can solve them simultaneously. The first equation can be rearranged to express \( y \) in terms of \( x \): \[ y = \frac{3}{4} x - 3. \] Next, we can substitute this expression for \( y \) into the second equation: \[ 4x - 3\left(\frac{3}{4}x - 3\right) = 5. \] Solving this gives us a value for \( x \), which we can then use to find \( y \). If there’s a consistent \( (x, y) \) solution, then the system has a solution. In this case, yes, the system has a unique solution! To find the solution, conduct the substitution and simplify the second equation, leading to a value of \( x \). Then plug it back to find \( y \).