25pts ryan, jessica, and mark each solved this system of equations. all of their answers are different. find and explain the mistakes. what is the correct answer? y = 3x + 2 6x – 2y = 10

Mark has the correct answer.  Ryan and Jessica both made mistakes in their calculations with computing negative integers.  

Step-by-step explanation:

Looking at the graphing method first, we need to get both equations into the slope-intercept format (y = mx + b) to compare these variables:

y = 3x + 2  has a slope = 3 and y-intercept = 2

6x - 2y = 10 can also be written as -2y = -6x + 10 or y = 3x - 5 which also has a slope = 3, but a y-intercept = -5

Since both lines have the same slope, then we know they must be parallel and therefor, there is no solution.  

Ryan used elimination to solve his system, however, when converting both equations to standard form (Ax + By = C), he forgot to make the '3x' from the first equation negative, or '-3x', which made the rest of his calculations incorrect.

Jessica used matrices and made the determinant for the system, x and y.  Jessica set up her determinant correctly, however, when solving the system determinant, she did not multiply 3 x -2 correctly and instead put positive 6 instead of -6 which made her answer 12 instead of 0.  

oof

step-by-step explanation:

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0