Respuesta :
Answer:
John is correct. Solution of the system of equations will be the empty set.
Step-by-step explanation:
Equations of the system of two lines are,
y = 3x - 2 --------(1)
6x - 2y = 4
(6x - 2y) - 6x = 4 - 6x
-2y = 4 - 6x
2y = 6x - 4
[tex]\frac{2y}{2}=\frac{6x-4}{2}[/tex]
y = 3x - 2 -------(2)
We have to solve these equations for the solutions.But the equations are same so there will be no solution.
Therefore, John is correct. Solution of the system of equations will be an empty set.
Answer:
John is not correct.
Step-by-step explanation:
We have been given two equations [tex]y = 3x-2\text{ and }6x-2y = 4[/tex]. John graphed the two equations on his graphing calculator. Because he saw only one line, John wrote that the answer to the system is the empty set. We are asked to determine whether John is correct or not.
Let us solve 2nd equation in slope-intercept form.
[tex]6x-2y = 4[/tex]
[tex]6x-6x-2y = 4-6x[/tex]
[tex]-2y=-6x+4[/tex]
Now, we will divide both sides by -2 as:
[tex]\frac{-2y}{-2}=\frac{-6x}{-2}+\frac{4}{-2}[/tex]
[tex]y=3x-2[/tex]
Since both equation represent same line, that's why John only got one line on graphing calculator. All the points on line [tex]y=3x-2[/tex] will be on [tex]6x-2y=4[/tex] and lines have infinitely many solutions.
Since the solution of the both equations is all points on the line, therefore, John is not correct.
