Question
Which of these graphs shows that the linear system 3x+2y=12 and y= -3/2x+6 has infinite number of solutions
Answers
GPT-4o mini
For a linear system to have an infinite number of solutions, the two equations must represent the same line. This means that they are equivalent, meaning one equation can be derived from the other.
1. The first equation is given as:
\[
3x + 2y = 12
\]
We can rearrange it into slope-intercept form (y = mx + b):
\[
2y = -3x + 12 \implies y = -\frac{3}{2}x + 6
\]
2. The second equation is:
\[
y = -\frac{3}{2}x + 6
\]
Both equations are actually the same line, as shown by manipulating the first equation into the same form as the second. Therefore, if you see a graph depicting these two equations, it will show that they coincide, representing the same line.
Look for a graph where both equations lie on top of each other (the same line). It should display that any point on that line is a solution to both equations, indicating an infinite number of solutions.
If you had specific graphs to assess, you would choose the one where both equations overlap entirely.
1. The first equation is given as:
\[
3x + 2y = 12
\]
We can rearrange it into slope-intercept form (y = mx + b):
\[
2y = -3x + 12 \implies y = -\frac{3}{2}x + 6
\]
2. The second equation is:
\[
y = -\frac{3}{2}x + 6
\]
Both equations are actually the same line, as shown by manipulating the first equation into the same form as the second. Therefore, if you see a graph depicting these two equations, it will show that they coincide, representing the same line.
Look for a graph where both equations lie on top of each other (the same line). It should display that any point on that line is a solution to both equations, indicating an infinite number of solutions.
If you had specific graphs to assess, you would choose the one where both equations overlap entirely.