To solve the system of equations
\[ \begin{cases} y = -5x + 6 \ y = 3x - 2 \end{cases} \]
we can set the two equations for \(y\) equal to each other:
\[ -5x + 6 = 3x - 2 \]
Now, we will solve for \(x\). First, we can add \(5x\) to both sides:
\[ 6 = 3x + 5x - 2 \]
This simplifies to:
\[ 6 = 8x - 2 \]
Next, we can add \(2\) to both sides:
\[ 6 + 2 = 8x \] \[ 8 = 8x \]
Now, divide both sides by \(8\):
\[ x = 1 \]
Now that we have the value of \(x\), we can substitute it back into either of the original equations to find \(y\). We’ll use the first equation:
\[ y = -5(1) + 6 \] \[ y = -5 + 6 \] \[ y = 1 \]
Thus, the solution to the system of equations is:
\[ x = 1, \quad y = 1 \]
In summary:
\[ x = 1 \] \[ y = 1 \]
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