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

Answer

A. Many solution

Step by step explanation

Points on line 1 : (-3, 6) and (3, 4)

Points on line 2: (-6, 7) and  (9, 2)

Now let's find the slope of the line 1

Slope formula =

Slope of line 1 = (4 - 6) / (3 - (-3)

= -2/(3 + 3)

= -2/6

Slope of line 1 = -1/3

The equation of the line y - y 1 = m(x - x1)

y - 6 = -1/3 (x - (-3))

y -6 = -1/3 (x + 3)

y -6 = -1/3x - 1

y = -1/3x + 5

Slope of line 2 = (2 - 7) / (9 -(-6))

= -5/(9 + 6)

= -5/15

Slope of line 2 = -1/3

The equation of line

y - y1 = m(x - x1)

y - 7 = -1/3(x - (-6))

y - 7 = -1/3(x + 6)

y -7 = -1/3 x - 2

y = -1/3 x + 5

The line 1 and line 2 have the same slopes and the same y-intercept. Both are the same equation. Therefore, there will be many solution.

Answer : A. 0 Solution

Thank you.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

the answer is 24

step-by-step explanation: