Ineed with this, somebody me
the coordinates below represent two linear equations.
how many solutions does this system of equations have?
line 1
x y
–3 6
3 4
line 2
x y
–6 7
9 2
a.
0
b.
exactly 1
c.
exactly 2
d.
infinitely many

The soluttion would be the interesctions of the lines

two line can only intercect in only 0 or one or all of the points (when the 2 lines are equal)

so the answers could be A,B, D

then we solve for the slope-intercept form

y=mx+b m=slope=(y1-y2)/(x1-x2)
and b=y intercept
line one
(6-4)/(-3-3)=2/-6=-1/3
y=-1/3x+b
subsitute -3 for x and 6 for y
6=-1/3(3)+b
6=-1+b
7=b

y=-1/3x+7 is the equation of the first line

second line(7-2)/(-6-(9))=5/-15=-1/3
y=-1/3x+b
subsitue -6 for x and 7 for y
7=-1/3(-6)+b
7=2+b
5=b
y=-1/3x+6

the equations are
y=-1/3x+7
y=-1/3x+6

since they have the same slope, they are parrelell, and since they do not have the same y-intercept, they are not on the same level

the do not intercect in any point

the answer is A, zero points/no solution

Ithink it’s d as the answer.