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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.
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What is a system of linear equations in two variables?
They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.
How many types of solutions of a system of two linear equations in two unknowns can exist?
There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
What are the common characteristic between simultaneous linear equations in 2 unknowns which have no solutions?
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
Is it possible for a system of linear equations to have zero solutions?
Yes, a system of linear equations can have zero solutions, which is known as an inconsistent system. This occurs when the equations represent parallel lines that never intersect, meaning there is no point that satisfies all equations simultaneously. A common example is the system represented by the equations (y = 2x + 1) and (y = 2x - 3), which are parallel and thus have no solutions.
What are linear equations with the same solutions called?
They are called simultaneous equations.
What is a system of linear equations in two variables?
They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.
How many types of solutions of a system of two linear equations in two unknowns can exist?
There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
What are the common characteristic between simultaneous linear equations in 2 unknowns which have no solutions?
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
What are inifintly equations?
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
Is it possible for a system of linear equations to have zero solutions?
Yes, a system of linear equations can have zero solutions, which is known as an inconsistent system. This occurs when the equations represent parallel lines that never intersect, meaning there is no point that satisfies all equations simultaneously. A common example is the system represented by the equations (y = 2x + 1) and (y = 2x - 3), which are parallel and thus have no solutions.
What are linear equations with the same solutions called?
They are called simultaneous equations.
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 is cramer rule?
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
How many solutions does linear equation in two variable have?
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
It is possible for a system of linear equations to have an infinite number of solutions.?
Yes, a system of linear equations can have an infinite number of solutions when the equations represent the same line or when they are dependent on each other. This typically occurs in systems with fewer independent equations than variables, leading to free variables that allow for multiple solutions. In such cases, the solutions can be expressed in terms of parameters, indicating a whole line or plane of solutions rather than a single point.
What are the possible solutions for a pair of linear equation?
Any system of linear equations can have the following number of solutions: 0 if the system is inconsistent (one of the equations degenerates to 0=1) 1 if the system is linearly independent infinity if the system has free variables and is not inconsistent.
