Question

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Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find \(m\) and \(b\) for \(y = 5x+9\)

For the equation \(y = 5x + 9\), comparing with \(y=mx + b\), we can see that \(m = 5\) and \(b=9\).

Step3: Find \(m\) and \(b\) for \(y = 9x + 5\)

For the equation \(y=9x + 5\), comparing with \(y = mx + b\), we can see that \(m = 9\) and \(b = 5\).

Step4: Determine the number of solutions

Since the slopes \(m_1=5\) and \(m_2 = 9\) are not equal, the two lines are not parallel and will intersect at exactly one point. So the number of solutions is one.

Answer:

For \(y = 5x+9\): \(m=\boldsymbol{5}\), \(b=\boldsymbol{9}\)
For \(y = 9x + 5\): \(m=\boldsymbol{9}\), \(b=\boldsymbol{5}\)
Number of solutions: \(\boldsymbol{one}\)