The perimeter os a tennis court is 228 feet and the lenght is 42 feet longer than the width. Write a linear system. Let w be the width of the tennis court and let l be the lenght of the tennis court. Graph the linear system.
W = width
W + 42 = length
P = 2W + 2L
228 = 2(W) + 2(W + 42)
Solve for W
W + 42 = Length
To write a linear system for this problem, we can start by setting up two equations based on the given information.
1. The perimeter of a rectangle is given by the formula: P = 2(length + width)
2. We are told that the length is 42 feet longer than the width, so we can express the relationship as: l = w + 42
Now, let's write the linear system:
Equation 1: P = 2(l + w)
Equation 2: l = w + 42
To graph the linear system, we need to rewrite the equations in slope-intercept form, which is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Equation 1: P = 2(l + w)
=> P = 2w + 2l
=> P/2 = w + l/2
=> l/2 = -w/2 + P/2
Equation 2: l = w + 42
=> l - w = 42
Now, we can rewrite both equations in slope-intercept form:
Equation 1: l/2 = -w/2 + P/2
=> l = -w + P/2
Equation 2: l - w = 42
To graph the linear system, we can plot points on a coordinate plane using the slope-intercept form equations. Unfortunately, as the equations involve three variables (P, l, and w), we cannot directly graph it on a 2D plane. However, we can manipulate the equations to create an equation with only two variables in order to graph it.
Combining the two equations, we can eliminate l:
From Equation 2: l = w + 42
Substituting into Equation 1: -w + P/2 = w + 42
Simplifying: -w - w = 42 - P/2
Combining like terms: -2w = 42 - P/2
Dividing both sides by -2: w = (P/2 - 42)/2
Now, we can graph the equation w = (P/2 - 42)/2 on a coordinate plane. The x-axis represents the width (w), and the y-axis represents the perimeter (P). The graph will be a straight line.
However, since the length (l) cannot be directly represented on this graph, we can choose some values for the perimeter (P), calculate the corresponding width (w) using the equation, and then calculate the length (l) using l = w + 42.
By plotting these points, we can visualize the relationship between the width, length, and perimeter of the tennis court.