An equation of a straight line is called a linear equation. When we work with two or more linear equations it is called system of linear equation, the point of intersection of these lines is the solution. The possible number of solutions of a given system of equations depend on how the lines are, if they intersect at only one point there would be one solution, if the lines are parallel then there would be no solutions and if the line is the same then there is possibility of infinite number of solutions which is a rare case.
We can find the solutions of the given linear equations using one of the following methods, graphing method, substitution method, and elimination method. Even a graphic calculator can be used to find the solution.
An equation of the form a1x1+ a2x2 + a3x3+…….+ anxn=b where x1, x2, x3,……xn are the variables and a1, a2,a3,….,an and b are constants which are either real or complex numbers is called a linear equation. Here ai is the coefficient of the variable xi and b is a constant term in the equation.
Coming to a system of linear equations, they are linear equations which have the same variables. For instance, a linear system of m equations in n variables y1, y2, y3,……yn can be given as, a11y1 + a12y2+a13y3+………+a1nyn= b1;
a21y1 + a22y2+a23y3+………+a2nyn= b2 and so on, am1y1 + am2y2+am3y3+………+amnyn= bm. For any system of linear equations there are three possibilities of solutions, a unique solution, no solutions or infinitely many solutions. If the linear system has at least one solution it is said to be consistent and if it has no solution then it is said to be inconsistent. Example of linear systems of equations in two variables is, y=3x+2; y=5x-10
System of Linear Equation solver, while solving linear-equations with more than two variables graphing method of solving cannot be used so in such cases we use algebraic method of substitution or elimination. In substitution method first one of the equations is written in the form something like ‘y=….’ Where y is one of the variables, next step would be to replace this ‘y’ value in the other equation and then solve the equations.
This method is repeated if necessary. In Elimination method a stepwise elimination of variables is done till there is only one variable left, the value of this variable is substituted in one of the linear equations to get the value of another variable. The method is repeated to get the final solution.
We can find the solutions of the given linear equations using one of the following methods, graphing method, substitution method, and elimination method. Even a graphic calculator can be used to find the solution.
An equation of the form a1x1+ a2x2 + a3x3+…….+ anxn=b where x1, x2, x3,……xn are the variables and a1, a2,a3,….,an and b are constants which are either real or complex numbers is called a linear equation. Here ai is the coefficient of the variable xi and b is a constant term in the equation.
Coming to a system of linear equations, they are linear equations which have the same variables. For instance, a linear system of m equations in n variables y1, y2, y3,……yn can be given as, a11y1 + a12y2+a13y3+………+a1nyn= b1;
a21y1 + a22y2+a23y3+………+a2nyn= b2 and so on, am1y1 + am2y2+am3y3+………+amnyn= bm. For any system of linear equations there are three possibilities of solutions, a unique solution, no solutions or infinitely many solutions. If the linear system has at least one solution it is said to be consistent and if it has no solution then it is said to be inconsistent. Example of linear systems of equations in two variables is, y=3x+2; y=5x-10
System of Linear Equation solver, while solving linear-equations with more than two variables graphing method of solving cannot be used so in such cases we use algebraic method of substitution or elimination. In substitution method first one of the equations is written in the form something like ‘y=….’ Where y is one of the variables, next step would be to replace this ‘y’ value in the other equation and then solve the equations.
This method is repeated if necessary. In Elimination method a stepwise elimination of variables is done till there is only one variable left, the value of this variable is substituted in one of the linear equations to get the value of another variable. The method is repeated to get the final solution.
No comments:
Post a Comment