Idon’t really understand this type of stuff so .

For 1 and 2, you plot both lines, and wherever they intersect is the solution to the system. Given the equation of a line, I think the easiest way to plot it is to find two points on the line, then draw a line through them. For example, if , then when , you get ; when , you get . So plot the points (0, -1) and (1, 4), then strike a line through.

1. Notice that dividing both sides of by 2 returns , same as the first equation. So the system of equations reduces to one equation, which can have an infinite number of solutions. (This is because for any choice of or , you can always find a corresponding value for the other variable.)

2. See attached image. is given by the purple line.

For 3-6, you have several options. The two simplest methods of solving them are by substitution or elimination.

3. Like with (1), notice that dividing both sides of the first equation by 2 gives , so there will be an infinite number of solutions.

4. (by substitution) Since , we can replace in the second equation:

but this is false, so there are no solutions to this system.

5. (by substitution) Since , in the first equation we have

Then back in the second equation we find

So (-4, -3) is the only solution here.

6. (by substitution) Notice that the left hand sides of both equations are the same, so we end up with 7 = 12, but this is false, so no solution exists.

equal to

step-by-step explanation:

- "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."