Slove the system of equations y=2x-3 y=x^2-3

(0, - 3) or (2, 1)

Since both equations express y in terms of x we can equate them

x² - 3 = 2x - 3

subtract 2x from both sides

x² - 2x - 3 = - 3

add 3 to both sides

x² - 2x = 0

take out a common factor of x

x(x - 2) = 0

equate each factor to zero and solve for x

x = 0 or x - 2 = 0 ⇒ x = 2

substitute values of x into y = 2x - 3 for corresponding values of y

x = 0 → y = 0 - 3 = -3 ⇒ (0, -3)

x = 2 → y = 4 - 3 = 1 ⇒ (2, 1)

- "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."

do you have a picture of the table