Question

y = 11x
x + y = 60
a group of related linear equations is called a system of linear equations.
where do the lines intersect?
(6, 60) (6, 55)
(5, 55) (5, 60)
chart with x-axis chaperones, y-axis students, lines x + y = 60 and y = 11x

Explanation:

Step1: Analyze the intersection point

The intersection of two lines is the point that satisfies both equations. From the graph, we can see the lines \(y = 11x\) and \(x + y=60\) intersect where \(x = 5\) (from the x - axis label "Chaperones" at 5) and we can check the y - value. For \(y = 11x\), when \(x = 5\), \(y=11\times5 = 55\). Also, for \(x + y=60\), when \(x = 5\), \(y=60 - 5=55\). So the intersection point is \((5,55)\).

Step2: Match with the options

Looking at the options: \((6,60)\) does not satisfy \(y = 11x\) (since \(11\times6 = 66
eq60\)), \((6,55)\) does not satisfy \(x + y=60\) (since \(6 + 55=61
eq60\)), \((5,60)\) does not satisfy \(y = 11x\) (since \(11\times5 = 55
eq60\)), and \((5,55)\) satisfies both \(y = 11x\) ( \(11\times5 = 55\)) and \(x + y=60\) ( \(5+55 = 60\)).

Answer:

\((5,55)\)