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Where are solutions to a system seen on the graph?
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.
What is the midpoint equation?
Midpoint equation also called midpoint formula is the formula to identify the middle point of the two end points. The formula for midpoint is ( {X2 + X1}/2 , {Y2 + Y1}/2 ).
What are equations with the same solution?
Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.
What is the equation of the line that contains the points -3 2 and 5 -5?
If you mean points of (-3, 2) and (5, -5) then the equation works out as 8y = -7x-5
How are graphs and equations related?
The graph of an equation represents the solution set of the equation, that is all the solutions of the equation are points that lie on the graph and all the points that lie on the graph are solutions of the equation.
What is the set of all points representing solutions?
The solution set is the set of all points representing solutions.
How are the graph of an equation and the set of all solutions of an equation related?
The coordinates of every point on the graph, and no other points, are solutions of the equation.
What is the place where 2 curves meet?
The points of intersection. The coordinates of such points will be the solutions to the simultaneous equations representing the curves.
How many solutions does an equation have when you isolate the variable and it equals constant?
As many solutions as there are points in the domain.
How do you use a graph to determine 3 solutions of an equation?
To determine three solutions of an equation using a graph, first plot the equation on a coordinate plane. Identify the points where the graph intersects the x-axis; these x-values represent the solutions of the equation. Each intersection point corresponds to a solution, so you can read the x-coordinates of these points to find the three solutions. Ensure that the graph is drawn accurately for precise identification of the solutions.
When system of linear equations is graphed how is the graph of each equation related to the solutions of that equation?
When a system of linear equations is graphed, each equation is represented by a straight line on the coordinate plane. The solutions to each equation correspond to all the points on that line. The intersection points of the lines represent the solutions to the entire system; if the lines intersect at a point, that point is the unique solution. If the lines are parallel, there are no solutions, and if they overlap, there are infinitely many solutions.
When a system of linear equations is graphed how is the graph of each equation related to the solutions of that equation?
When a system of linear equations is graphed, each equation represents a line in a coordinate plane. The solutions to each equation correspond to the points on that line. The intersection points of the lines represent the solutions to the system as a whole, indicating where the equations are satisfied simultaneously. If the lines intersect at a single point, there is a unique solution; if they are parallel, there are no solutions; and if they coincide, there are infinitely many solutions.
What information does the graph of a function provide with respect to the algebraic equation?
The coordinates of the points on the curve represent solutions of the equation.
What is 2x-3y equals -2?
This is an equation of a line. There are an infinite number of solutions which are all points on the line. It is a linear equation.
What are the zeros of a parabola?
They are the x-values (if any) of the points at which the y-value of the equation representing a parabola is 0. These are the points at which the parabola crosses the x-axis.
Explain how the number of solutions for a quadratic equation relates to the graph of the function?
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
What set of points whose coordinates satisfy the equation is called?
The set of points whose coordinates satisfy a given equation is called the graph of the equation. For example, in the case of a linear equation, the graph is a line, while for a quadratic equation, it is a parabola. This collection of points visually represents the relationship described by the equation in a coordinate system.
