how many solutions does the linear system have? x=3 y= -2
If you mean how many straight lines pass through the point (3,-2), there are an infinite number. You gave a point, but no slope, so lines can go through there at any angle from 0 to 180 and all angles in between.
So there wouldnt just be one or two? so it would be undetermined, right?
Yes, if just have one point and no slope or second point given, the slope is undetermined so the line is undeterminable.
Thank you, I appreciate it. :)
To determine the number of solutions for a linear system, we need to assess the relationship between the equations. In this case, the given equations are:
x = 3
y = -2
Since each equation represents a separate line, we can plot them on a graph to see if they intersect at a single point, are parallel, or coincide (representing infinitely many solutions).
For the equation x = 3, the line will be vertical and intersect the y-axis at x = 3.
For the equation y = -2, the line will be horizontal and pass through y = -2 at every x-coordinate.
However, when we plot these lines, we notice that they intersect at the point (3, -2). This means that there is exactly one solution to this linear system. Additionally, we can also conclude that the lines are neither parallel nor coincident, as they intersect at a single point.
In summary, the given linear system x = 3 and y = -2 has one unique solution, which is (3, -2).