Why is the point ( 3, 4 ) the solution to this system of equations?
y= 1/3x + 3
y= 2x - 2

The answer to your question is because it is a solution of each equation.

Step-by-step explanation:

Data

Point (3,4)

Equation l     y = 1/3x + 3

Equation ll     y = 2x - 2

Process

1.- To test is a point is solution to a system of equations,

-Substitute the point in both equations

Equation l            4 = 1/3(3) + 3

                            4 = 1 + 3

                            4 = 4               The point is a solution because

                                                     4 = 4

Equation ll            4 = 2(3) - 2

                             4 = 6 - 2

                             4 = 4               This point is a solution for the second

                                                     equation but not for the first one.

2.- Conclusion

As the point is a solution of each equation, it is a solution of the system.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."