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Linear Equation in Two Variables
A linear equation in two variables is an equation that can be written in the form y = mx + b, where m and b are constants. This equation represents a line in a coordinate plane, and the slope of the line is m, and the y-intercept is b.
Definition
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
The solution for such an equation is a pair of values, one for x and one for y which further makes the two sides of an equation equal.
Solution of Linear Equations in Two Variables
The solution of linear equations in two variables, ax+by = c, is a particular point in the graph, such that when x-coordinate is multiplied by a and y-coordinate is multiplied by b, then the sum of these two values will be equal to c.
Basically, for linear equation in two variables, there are infinitely many solutions.
Linear Equation in Two Variables Example
A linear equation in two variables is an equation that can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
A linear equation in two variables can be used to solve for either x or y, depending on which is unknown. To solve for x, substitute y = 0 into the equation and solve for x. To solve for y, substitute x = 0 into the equation and solve for y.
Graphing of Linear Equation in Two Variables
A linear equation in two variables is a mathematical equation in which each equation is a straight line. In order to graph a linear equation in two variables, one must first determine the equation of the line. This can be done by solving for the y-intercept and the slope of the line. Once the equation has been determined, the graph can be plotted by using the points that satisfy the equation.
The equation of a line can be determined by solving for the y-intercept and the slope. The y-intercept is the point at which the line crosses the y-axis. The slope of the line is the rate of change in the y-direction. It can be determined by finding the change in y-value divided by the change in x-value.
Once the equation of the line has been determined, the graph can be plotted by using the points that satisfy the equation. The points can be plotted by using the coordinate grid. The x-coordinate is the first number in the pair and the y-coordinate is the second number in the pair. The points can be plotted by using the points that are given in the equation or by using a method known as interpolation. Interpolation is the process of estimating the value of a point that is not given in the equation. This can be done by using the points that are given in the equation.
