To determine if the point (0,3) is a solution to the given system of equations, we need to verify if it satisfies both equations:
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The first equation is given as: \[ 13x + y = 32 \]
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The second equation is given as: \[ y = -23x + 10 \]
Now, let's substitute \(x = 0\) and \(y = 3\) into both equations and check if they hold true.
For the first equation: \[ 13(0) + 3 = 32 \] This simplifies to: \[ 0 + 3 = 32 \quad \Rightarrow \quad 3 = 32 \] This is false, so the point (0,3) does not satisfy the first equation.
For the second equation: \[ 3 = -23(0) + 10 \] This simplifies to: \[ 3 = 0 + 10 \quad \Rightarrow \quad 3 = 10 \] This is also false, so (0,3) does not satisfy the second equation either.
Since the point (0,3) does not satisfy either of the two equations, we conclude that (0,3) is not a solution to the system of equations.
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