In order to solve a linear equation using matrices, express the given equations in standard form, with the variables and constants on respective sides. The solution of a system of equations can be solved using matrices. Solving System of Equations Using Matrices Methods I and II are the algebraic way of solving simultaneous equations and III is the graphical method. So, x = 1, y = 2 is the solution of given system of equations. We observe that the two lines intersect at (1,2). Plotting these points on the graph we can get the lines in a coordinate plane as shown below. We have two points C(-3, 0) and D( 3, 3). Similarly, find the at least two values of x and y satisfying equation -x + 2y = 3 x "The point of intersection of the two lines is the solution of the system of equations using graphical method."įind at least two values of x and y satisfying equation 3x + 4y = 11 x In this method, the solution of simultaneous equations is obtained by plotting their graphs. Solving System of Equations Using Graphical Method Multiplying Eqn(1) by 2 and Eqn(2) by 3, we get The coefficients of y are 3 and 2 LCM (3, 2) = 6 Using the elimination method to solve the system of equations, we eliminate one of the unknowns, by multiplying equations by suitable numbers, so as the coefficients of one of the variables become the same.
Solving System of Equations Using Elimination Method Hence, x = 9 and y = 4 is the solution of given system of equations.
Solving System of Equations Using Substitution Methodįor solving the system of equations using the substitution method given two linear equations in x and y, express y in terms x in one of the equations and then substitute it in 2nd equation. Let us understand 3 ways to solve a system of equations given the equations are linear equations in two variables. Similarly, for solving a system of equations in 3 variables, we will require at least 3 equations. To solve a system of equations in 2 variables, we need at least 2 equations. Infinite Many SolutionsĪ system of equations can have infinitely many solutions when there exists a solution set of infinite points for which L.H.S and R.H.S of an equation become equal, or in the graph straight lines overlap each other.Īny system of equations can be solved in different methods. No SolutionĪ system of equations has no solution when there exists no point where lines intersect each other or the graphs of equations are parallel.
Similarly, for a system of linear equations in two variables, the unique solution is an ordered pair (x, y) which will satisfy both the equations in the system. Let understand the concept of a unique solution using a linear equation in one variable, 4x = 8 has a unique solution x = 2 for which the L.H.S is equal to the R.H.S. The unique solution of a system of equations means that there exists only one value for the variable or the point of intersection of the lines representing those equations, on substituting which, L.H.S and R.H.S of all the given equations in the system become equal.įor example, we know that a linear equation in one variable will always have one solution. There can be different types of solutions to a given system of equations, The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true. We compute the values of the unknown variables still balancing the equations on both sides. Solving a system of equations means finding the values of the variables used in the set of equations.
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