Question

Which of the following is a solution for the system y = -3x + 5 and y = 2x + 5?

Answer 1

Take the first equation, y = -2x + 5

We know that this has a negative gradient as the x-coefficient is negative. This means it will be travelling from top left to bottom right.
We only need two points to plot a line, so we can use the x and y intercepts as it makes the maths easy substituting in 0! You could however, put in any number for x and obtain the y value to find a point on the line. Anyway, back to intercepts.
When x = 0,
y = -2(0) + 5 = 5
so the point (0, 5) is on the line.
When y = 0,
0 = -2x + 5
2x = 5
x = 2/5 = 0.4
So the point (0.4, 0) is also on the line.
Plot these 2 points and draw a line through them. Make the line as long as possible on your page.

Now consider the second equation. We need to find two points again.
When x = 0,
y = (1/2)(0) - 5
y = -5
So, (0, -5) is a point on the line.
When y = 0,
0 = (1/2)x - 5
(1/2)x = 5
x = 10.
So (10, 0) is a point on the line.
Plot these two points and draw a nice long line through them.

Now, the lines should cross somewhere, and this is the point of intersection. Simply read it off and there's your answer.

Answer 2

This is history not math. :P

Answer 3

lol, oops :)

Answer 4

Really?

Answer 5

i got a medal anyway though :).