Use a graph to determine the number of solutions the system has.
-$$\begin{array} { l }
2 x - 4 y = 6 \
6 x - 12 y = 19
\end{array}$$
A) One solution
B) No solution
C) Infinitely many solutions

Question

Use a graph to determine the number of solutions the system has.
-$$\begin{array} { l } 
2 x - 4 y = 6 \
6 x - 12 y = 19
\end{array}$$
A) One solution
B) No solution
C) Infinitely many solutions

Quizplus · Accepted Answer

The given system of equations is 2x - 4y = 6 and 6x - 12y = 19. If we simplify the second equation by dividing every term by 3, we get 2x - 4y = 19/3, which is not equivalent to the first equation (2x - 4y = 6). However, both equations represent lines with the same slope (since dividing the coefficients of x and y in the second equation by 3 gives the same ratio as in the first equation), but different y-intercepts, indicating that the lines are parallel and do not intersect. Therefore, there is no solution to the system.

Use a Graph to Determine the Number of Solutions the System