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What is equations that have the same solutions?
Simultaneous equations have the same solutions.
Can a system of two linear equations have exactly two solutions explain?
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
What are equations that have the same answer?
Simultaneous equations have the same solutions
If a system of equations is dependent how many solutions will it have?
Infinite simultaneous solutions. (The two equations represent the same line) OR If your in nova net the answer should be ( Many )
What is an equation that have the same solutions?
Simultaneous equations have the same solutions.
Why could a system of linear equations have two solutions?
A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.
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 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.
How many possible solutions can a system of two linear equations in two unknowns have?
A system of two linear equations in two unknowns can have three possible types of solutions: exactly one solution (when the lines intersect at a single point), no solutions (when the lines are parallel and never intersect), or infinitely many solutions (when the two equations represent the same line). Thus, there are three potential outcomes for such a system.
What systems of equations is infinitely many solutions?
A system of equations has infinitely many solutions when the equations represent the same line or plane. In a two-variable scenario, this occurs when both equations can be simplified to the same linear equation, meaning they are dependent. Graphically, this results in overlapping lines. For example, the equations (2x + 3y = 6) and (4x + 6y = 12) represent the same line and thus have infinitely many solutions.
What are linear equations with the same solutions called?
They are called simultaneous equations.
