Consider the following system of equations.

Question

{y = 3x − 5
{y = −x + 7
a. Are the graphs of the two lines intersecting lines, the same line, or parallel lines? Explain your reasoning.
b. How many solutions does the system have? Explain how you can tell without solving the system.

I know they're intersecting lines but because I graphed out the equation and I don't think that's what the school wants me to do.

Answer 1

All you have to do is look at the slopes of the two lines.
the first one has slope of 3
the 2nd has a slope of -1
So they clearly must intersect.

recall that in the form y = mx + b, m represents the slope

Answer 2

(a) they must intersect, since their slopes are different. Only parallel lines never intersect.
(b) surely you know how many times two lines can intersect. If not, look at your graph!