List the methods used for solving linear equations in two variables.
Linear equations are one of the most important concepts of mathematics which are used in various other fields in engineering and science to obtain values of different parameters and quantities. There are many ways to solve a linear equation. Let's have a look at those ways on this blog.
Answer: The methods used for solving linear equations in two variables are the graphing method, substitution method, elimination method and matrix method.
Let's understand these methods in detail.
There are four major methods using which we can solve linear equations in two variables:
- Graphing method - This method involves plotting the graphs of both the equations on the cartesian plane. The point where both the lines intersect is the solution to that particular system of equation. This is only helpful when the solutions are integers.
- Substitution method - This method involves solving one linear equation in terms of one variable and then substituting that value into the other equation to solve the problem. For example, to solve the system of equations: x + y = 10 and x - y = 5, we first solve the second equation for y, that is, y = x - 5, and then substitute this value of y in terms of x into the first equation to get the value of x = 7.5, and hence the value of y = 2.5.
- Elimination method - In this method, we eliminate one of the variables to find the value of the other variable. Then we substitute the value of that variable into one of the given equations to find the value of the remaining variable.
- Matrix method - In this method, we represent both the equations into matrices of the form AX = B, where A is a 2 × 2 coefficient matrix, X is the 2 × 1 variable matrix and B is the 2 × 1 solution matrix, and then solve them by finding the inverse of the matrix A.