The coordinates below represent two linear equations.
how many solutions does this system of equations have?
line 1
x y
–2 7
0 6
line 2
x y
3 0
0 –3
a.
0
b.
exactly 1
c.
exactly 2
d.
infinitely many

Find the equations of the lines in slope-intercept form which is y=mx+b where m=slope b=y intercept
the choices:
0 solutions: means the lines don't intercect at all, meaning same slope but different y intercept or they ar paralell
1 solution: lines intercect in 1 point
2 solutions: curvy line with a straight line thorugh middle
infinetly solutions: same line
 

to find slope you do
slope=(y1-y2)/(x1-x2)
first line is
(2,-7)
(0,6)
(x,y)
x1=2
y1=-7
x2=0
y2=6
subsitute
(-7-6)/(2-0)=-13/2
slope=-13/2
subsitute
y=-13/2x+b
subsitute one of the points
(0,6)
x=0
y=6
6=-13/2(0)+b
6=0+b
6=b
y=-13/2+6

now solve for the other equation

(3,0)
(0,-3)
x1=3
y1=0
x2=0
y2=-3
subsitute
(0-(-3))/(3-0)=(0+3)/(3)=3/3=1
y=1x+b
subsitute
(3,0)
x=3
y=0
0=1(3)+b
0=3+b
subtract 3
-3=b
y=x-3

we have the lines
y=-13/2x-6 and
y=x-3
solve for a common solution
y=x-3 and y=-13/2x-6 therefor
x-3=-13/2x-6
add 6 to both sides
x+3=-13/2x
multiply both sides by -2
-2x-6=13x
add 2x to both sides
-6=15x
divide both sides by 15
-2/5=x
subsitute
y=x-3
y=-2/5-3
y=-3 and 2/5 or -17/5
the solution is (-2/5, -17/5)
there is only one solution
the answer is B