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If two linear equations are in standard form how can you tell that the graphs are parellel?
If the slopes are the same on both graphs, they are parallel, and will never touch.
What is the relation between straight lines and linear equations?
The graph, in the Cartesian plane, of a linear equation is a straight line. Conversely, a straight line in a Cartesian plane can be represented algebraically as a linear equation. They are the algebraic or geometric equivalents of the same thing.
Can a linear programming problem have multiple optimal solutions?
When solving linear prog. problems, we base our solutions on assumptions.one of these assumptions is that there is only one optimal solution to the problem.so in short NO. BY HADI It is possible to have more than one optimal solution point in a linear programming model. This may occur when the objective function has the same slope as one its binding constraints.
How are math expressions and math equations the same?
They are the same except equations use the equal sign =
How do you solve a system of linear equations by graphing?
When you are solving a system of linear equations, you are looking for the values for the unknown variables (usually named x and y) that make each equation in the system true. Instead of using algebraic substitution or elimination, you can use graphing to find the variables. If you graph each equation on the same graph, the point where the graphs cross is the answer, which should be given as an ordered pair in the form (x,y). If the graphs do not cross anywhere (for example, parallel lines) then there is no solution. If the graphs of two lines end up being the same line, then there are an infinite number of solutions. You must know how to graph a line in order to use this method.
What are two or more linear equations using the same variables called?
A system of linear equations.
What does a graph with infinitely many solutions look like?
they have same slop.then two linear equations have infinite solutions
Why Two dependent simultaneous linear equations have infinite solutions?
Two dependent linear equations are effectively the same equation - with their coefficients scaled up or down.
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 are equations that have the same answer?
Simultaneous equations have the same solutions
What are the three types of possible solutions to a system of equations?
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
What does it mean if there are an infinite number of solutions for a system of linear equations?
It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
What is an equation that have the same solutions?
Simultaneous equations have the same solutions.
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
What is a group of linear equations that use the same variables?
a system of equations
What are the possible solutions for a system of equations?
The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
