X minus 3y equals -3 and 6x plus 2y equals -12What type of lines are these?

Answer 1

Both of these equations describe straight lines in the xy-plane. At the y-axis x=0 and at the x-axis y=0. So, by substituting in x=0, we can find where the two lines cross the y-axis and, by substituting in y=0, we can find where they cross the x-axis. For the first line:
x - 3y = -3
(sub in x=0)
0 - 3y= -3
(divide both sides by -3)
y=1 ----> so this line crosses the y-axis at y=1 only.
By following a similar process we can find that this line crosses the x-axis at x=-3 and that the second line, 6x + 2y = -12, crosses the x and y axes at x=-2 and y=-6respectively.

If the two lines cross each other then, at some point in the xy-plane, their x and y values will be equal, meaning we can rearrange one equation and substitute it into the second one:

Rearrange x - 3y = -3 to give:
x = 3y - 3
So we can substitute 3y - 3 into the second equation, 6x + 2y = -12, giving:
6(3y - 3) + 2y = -12
(multiply out the bracket and collect terms)
20y - 18 = -12
(add 3 to both sides and then divide both sides by 20)
y= 6/20 = 0.3
(sub this back into x= 3y - 3 to find x)
x=-2.1
So, the two lines cross each other at the point (-2.1, 0.3)