To determine how many solutions there are for the system of equations, we first need to rewrite both equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
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The first equation is \(3y = 3x + 6\). We can divide every term by 3 to simplify it: \[ y = x + 2 \]
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The second equation is already in slope-intercept form: \[ y = x + 2 \]
Now, we see that both equations are identical: \[ y = x + 2 \] This means they represent the same line.
Since both equations yield the same line, they coincide, leading to an infinite number of solutions. Every point on the line \(y = x + 2\) is a solution to the system.
Thus, the answer is Infinite solutions.