Linear Equation in two variables -
Linear Equations in Two Variables is a course that discusses about equations limited to linear equations in one variable. Linear equations which have two variables are common, and the solution involves extending some of the procedures which have already been introduced. A linear equation of two variables is of the form ax + by = c, where a is not equal to 0 and b is not equal to 0
Solution of the linear Equation -
Below are the sample solution of the linear Equation thus will also help us on how to graph linear equations
Problem - Find four different solutions of the equation x + 2y = 6.
Solution - By inspection, x = 2, y = 2 is a solution because for x = 2, y = 2
x + 2y = 2 + 4 = 6
Now, let us choose x = 0. With this value of x, the given equation reduces to 2y = 6 which has the unique solution y = 3. So x = 0, y = 3 is also a solution of x + 2y = 6. Similarly, taking y = 0, the given equation reduces to x = 6. So, x = 6, y = 0 is a solution of x + 2y = 6 as well. Finally, let us take y = 1. The given equation now reduces to x + 2 = 6, whose solution is given by x = 4. Therefore, (4, 1) is also a solution of the given equation. So four of the infinitely many solutions of the given equation are: (2, 2), (0, 3), (6, 0) and (4, 1).
Remark : Note that an easy way of getting a solution is to take x = 0 and get the corresponding value of y. Similarly, we can put y = 0 and obtain the corresponding value of x.
Linear Equations in Two Variables is a course that discusses about equations limited to linear equations in one variable. Linear equations which have two variables are common, and the solution involves extending some of the procedures which have already been introduced. A linear equation of two variables is of the form ax + by = c, where a is not equal to 0 and b is not equal to 0
Solution of the linear Equation -
Below are the sample solution of the linear Equation thus will also help us on how to graph linear equations
Problem - Find four different solutions of the equation x + 2y = 6.
Solution - By inspection, x = 2, y = 2 is a solution because for x = 2, y = 2
x + 2y = 2 + 4 = 6
Now, let us choose x = 0. With this value of x, the given equation reduces to 2y = 6 which has the unique solution y = 3. So x = 0, y = 3 is also a solution of x + 2y = 6. Similarly, taking y = 0, the given equation reduces to x = 6. So, x = 6, y = 0 is a solution of x + 2y = 6 as well. Finally, let us take y = 1. The given equation now reduces to x + 2 = 6, whose solution is given by x = 4. Therefore, (4, 1) is also a solution of the given equation. So four of the infinitely many solutions of the given equation are: (2, 2), (0, 3), (6, 0) and (4, 1).
Remark : Note that an easy way of getting a solution is to take x = 0 and get the corresponding value of y. Similarly, we can put y = 0 and obtain the corresponding value of x.
