Question
to determine which pair of equations form a system
with one solution, no solution, or infinite solutions.
y=–2x+3
with one solution, no solution, or infinite solutions.
y=–2x+3
Answers
GPT-4o mini
To determine the relationship between the equation you provided, \(y = -2x + 3\), and another equation (to form a system of equations), we need to analyze the two equations together.
We categorize systems of linear equations based on their graphical representations:
1. **One solution**: The lines intersect at one point. This occurs when the two equations have different slopes.
2. **No solution**: The lines are parallel and do not intersect. This occurs when the two equations have the same slope but different y-intercepts.
3. **Infinite solutions**: The lines are the same line. This occurs when the two equations have the same slope and the same y-intercept.
Let’s say you provide another linear equation, say \(y = mx + b\). Then we can analyze based on the value of \(m\) (the slope) and \(b\) (the y-intercept) of that second equation compared to the first equation \(y = -2x + 3\) (which has a slope of -2).
If you give an additional equation, I can help determine which case it falls into.
We categorize systems of linear equations based on their graphical representations:
1. **One solution**: The lines intersect at one point. This occurs when the two equations have different slopes.
2. **No solution**: The lines are parallel and do not intersect. This occurs when the two equations have the same slope but different y-intercepts.
3. **Infinite solutions**: The lines are the same line. This occurs when the two equations have the same slope and the same y-intercept.
Let’s say you provide another linear equation, say \(y = mx + b\). Then we can analyze based on the value of \(m\) (the slope) and \(b\) (the y-intercept) of that second equation compared to the first equation \(y = -2x + 3\) (which has a slope of -2).
If you give an additional equation, I can help determine which case it falls into.