Question

I WILL FAN !!!!!!! AND MEDAL!!!!
The coordinates below represent two linear equations.



How many solutions does this system of equations have?


Line 1
x y
–1 6
0 4

Line 2
x y
0 7
1 5





A.


0


B.


exactly 1


C.


exactly 2


D.


infinitely many

Answer 1

LINE 1.
find slope of the line using slope formula and points
slope (m) = (y2 - y1) / (x2 - x1)
(-1,6)...x1 = -1 and y1 = 6
(0,4)...x2 = 0 and y2 = 4
now we sub
slope(m) = (4 - 6) / (0 - 1)
slope(m) = -2/-1
slope = 2
now we will find the equation of the line by using y = mx + b and 1 set of points...it does not matter which set...(-1,6)...x = -1 and y = 6
slope (m) = 2
now we sub and find b (the y intercept)
y = mx + b
6 = 2(-1) + b
6 = -2 + b
6 + 2 = b
8 = b
so this line is : y = 2x + 8
----------------------
LINE 2
do exactly the same thing
slope (m) = (5 - 7) / (1 - 0)
slope(m) = -2/1 or just -2

y = mx + b
slope(m) = -2
(0,7)...x = 0 and y = 7
now sub
7 = -2(0) + b
7 = 0 + b
7 = b
so this line is : y = -2x + 7
---------------------
so our 2 lines are :
y = 2x + 8 and y = -2x + 7

In y = mx + b form, the m stands for the slope and the b stands for the y intercept. We will now compare the slopes and the y intercepts.

Line 1 : slope = 2 and y intercept = 8
Line 2 : slope = -2 and y intercept = 7

Learn this :
If the slopes are the same and the y intercepts the same, it will have infinite solutions.
If the slopes are different, then there is 1 solution
If the slopes are the same and the y intercepts different, it will have 0 solutions

So knowing this, what do you think the answer is ?