If: y = x2-7x+8 and y = -x2+9x-6
Then: x2-7x+8 = -x2+9x-6
So: 2x2-16x+14 = 0 => x2-8x+7 = 0
Therefore: x = 1 and x = 7
By substitution: x =1, y = 2 and x = 7, y = 8
Points of intersection: (1, 2) and (7, 8)
The intersection of the individual graphs. In the simplest case, the graph for each equation consists of a line (or some curve); the intersection is the points where the lines or curves meet.
If: x -2y = 1 then x = 1+2y If: 3xy -y^2 = 8 then 3(1+2y)y -y^2 = 8 So: 3y+6y^2 -y^2 = 8 => 3y+5y^2 -8 = 0 Solving the above quadratic equation: y = 1 or y = -8/5 By substitution the points of intersection are at: (3, 1) and (-11/5, -8/5)
geometry
The points are (-1/3, 5/3) and (8, 3).Another Answer:-The x coordinates work out as -1/3 and 8Substituting the x values into the equations the points are at (-1/3, 13/9) and (8, 157)
Geometry
The points of intersection. The coordinates of such points will be the solutions to the simultaneous equations representing the curves.
You need two, or more, curves for points of intersection.
The points of intersection are: (7/3, 1/3) and (3, 1)
There are none. Those two curves do not intersect.
Points of intersection work out as: (3, 4) and (-1, -2)
Solutions may be closed or open regions or they may be points within a region (for example, grid points for integer solutions), or points of intersection between curves or between curves and the axes. It all depends on what the graphs and the solutions are.
The point at which two curves meet is called an "intersection point." At this point, the coordinates of both curves are the same, indicating that they share a common value. Intersection points can be found in various contexts, such as in algebra, geometry, and calculus, and they can represent solutions to equations or systems of equations.
The intersection of the individual graphs. In the simplest case, the graph for each equation consists of a line (or some curve); the intersection is the points where the lines or curves meet.
A geometric intersection refers to the point or set of points where two or more geometric figures, such as lines, curves, or surfaces, meet or overlap. In mathematics, this concept is often explored in geometry and topology, where it can involve determining the conditions under which shapes intersect or calculating the intersection points. For example, the intersection of two lines in a plane can yield a single point, while the intersection of two circles can result in two points, one point, or no points at all, depending on their relative positions.
The points of intersection of the equations 4y^2 -3x^2 = 1 and x -2 = 1 are at (0, -1/2) and (-1, -1)
If: x-2y = 8 and xy = 24 Then: x = 8+2y and so (8+2y)y = 24 => 8y+2y2-24 = 0 Solving the quadratic equation: y = -6 or y = 2 By substitution points of intersection: (-4, -6) and (12, 2)
If: x+y = 7 and x2+y2 = 25 Then: x = 7-y and so (7-y)2+y2 = 25 => 2y2-14y+24 = 0 Solving the quadratic equation: y = 4 and y = 3 By substitution points of intersection: (3, 4) and (4, 3)