Question

Start: (5,8), end: (7,2)
start: (6,8), end: (3,-7)
what is the solution to both equations?

Answer 1

Start: (5,8), end: (7,2)
start: (6,8), end: (3,-7)
what is the solution to both equations?
A (5, 3)
B (3, 5)
C no solution
D (2, 4)

Answer 2

The solution to both equations is the point where they intersect. To find this point, we need to solve the equations simultaneously.

For the first set of equations:
Start: (5,8), end: (7,2)

Slope = (change in y) / (change in x)
Slope = (2-8) / (7-5)
Slope = -6 / 2
Slope = -3

Using the point-slope form of a linear equation:
y - 8 = -3(x - 5)
y - 8 = -3x + 15
y = -3x + 23

For the second set of equations:
Start: (6,8), end: (3,-7)

Slope = (change in y) / (change in x)
Slope = (-7-8) / (3-6)
Slope = -15 / -3
Slope = 5

Using the point-slope form of a linear equation:
y - 8 = 5(x - 6)
y - 8 = 5x - 30
y = 5x - 22

Now we can solve these two equations together:
-3x + 23 = 5x - 22

Adding 3x to both sides and subtracting 23 from both sides:
-22 - 23 = 5x - 3x
-45 = 2x

Dividing both sides by 2:
x = -45/2
x = -22.5

Substituting x = -22.5 into one of the equations:
y = -3(-22.5) + 23
y = 67 - 22.5
y = 44.5

Therefore, the solution to both equations is (-22.5, 44.5).

Answer 3

To find the solution to both equations, we need to find the point of intersection between the two lines formed by these sets of points.

For the first set of points (5,8) and (7,2):
The slope of this line is (2 - 8) / (7 - 5) = -6 / 2 = -3
Using the point-slope form of a line, we have:
y - 8 = -3(x - 5)
y - 8 = -3x + 15
y = -3x + 23

For the second set of points (6,8) and (3,-7):
The slope of this line is (-7 - 8) / (3 - 6) = -15 / -3 = 5
Using the point-slope form of a line, we have:
y - 8 = 5(x - 6)
y - 8 = 5x - 30
y = 5x - 22

Now, we can set both equations equal to each other:
-3x + 23 = 5x - 22

Rearranging the equation, we have:
-8x = -45
x = 45/8

Substituting this value of x into either of the equations, we get:
y = -3(45/8) + 23
y = -135/8 + 23
y = -135/8 + 184/8
y = 49/8

Therefore, the point of intersection between the two lines is (45/8, 49/8). However, this point does not appear in the answer choices provided.

Thus, the correct answer is C) no solution.