1. An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.
2. Linear equations in one variable, of the type ax + b = 0, can also be expressed as linear equations in two variables. Since, ax + b = 0 ⇒ ax + 0y + b = 0.
3. A solution of a linear equation in two variables is a pair of values, one for x and one for y, which satisfy the equation.
4. The solution of a linear equation is not affected when:
i. The same number is added or subtracted from both sides of an equation.
ii. Multiplying or dividing both the sides of the equation by the same non-zero number.
5. A linear equation in two variables has infinitely many solutions.
6. Every point on the line satisfies the equation of the line and every solution of the equation is a point on the line.
7. A linear equation in two variables is represented geometrically by a straight line whose points make up the collection of solutions of the equation. This is called the graph of the linear equation.
8. x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.
9. The graph of x = k is a straight line parallel to the y-axis. For example, the graph of the equation x = 5 is as follows:
10. The graph of y = k is a straight line parallel to the x-axis.
Parent Tip: Review the logic above to help your child master the concept of linear equation in two variables worksheet.
