A linear equation is that type of equation in which the power of the variable or variables is 1. Let us take a closer look and study how to do linear equations in two variables. Obviously the degree of both the variables is 1 and such equations are also called straight line equations. The reason is the graph of such an equation is always a straight line.
A straight line equation can be expressed in different forms. The slope-intercept form is mostly used because it depicts more like a function. The specialty of a linear function is the rate of change of function is constant.
Linear equations in two variables examples can be many. The equation in the form 5x + 2y = 7 is called the standard form, the form y = 2x + 3 is known as slope-intercept form. In this the coefficient of ‘x’ indicates the slope (the rate of change) of the equation and the constant term indicates the value of the equation when x = 0.
The latter is also called as the y-intercept because it is the y-coordinate of the point graph where the graph of the equation intersects the y-axis.
There is another form called as intercept form which is not that common. (x/4) + (y/2) = 1 is an example of intercept form. The numbers below each variable gives the values of intercepts with the corresponding axes.
Now let us study about solving linear equations two variables. A single equation cannot have a unique solution because for every value of one variable, there can be a corresponding value of the other variable. Thus there can be infinite solutions. Having problem with Compound Inequalities Word Problems keep reading my upcoming posts, i will try to help you.
This type of solution is called as consistent and dependent. The same situation happens even if there is a set of two equations which are similar to each other.
In case of system of two equations of single degree, there is a possibility that no set of values of the variable can satisfy both the equations.
In such a case, the system has no solution and is called as inconsistent. Graphically the straight lines representing the equations are parallel.
But in most cases a system of two equations of single power variables have a unique solution. Such a system is referred as consistent and independent. That is, only one set of values of the variables can satisfy both the equations.
Graphically, the ordered pair of the point of intersection of the straight lines representing the equations is the solution set of the equations.
A straight line equation can be expressed in different forms. The slope-intercept form is mostly used because it depicts more like a function. The specialty of a linear function is the rate of change of function is constant.
Linear equations in two variables examples can be many. The equation in the form 5x + 2y = 7 is called the standard form, the form y = 2x + 3 is known as slope-intercept form. In this the coefficient of ‘x’ indicates the slope (the rate of change) of the equation and the constant term indicates the value of the equation when x = 0.
The latter is also called as the y-intercept because it is the y-coordinate of the point graph where the graph of the equation intersects the y-axis.
There is another form called as intercept form which is not that common. (x/4) + (y/2) = 1 is an example of intercept form. The numbers below each variable gives the values of intercepts with the corresponding axes.
Now let us study about solving linear equations two variables. A single equation cannot have a unique solution because for every value of one variable, there can be a corresponding value of the other variable. Thus there can be infinite solutions. Having problem with Compound Inequalities Word Problems keep reading my upcoming posts, i will try to help you.
This type of solution is called as consistent and dependent. The same situation happens even if there is a set of two equations which are similar to each other.
In case of system of two equations of single degree, there is a possibility that no set of values of the variable can satisfy both the equations.
In such a case, the system has no solution and is called as inconsistent. Graphically the straight lines representing the equations are parallel.
But in most cases a system of two equations of single power variables have a unique solution. Such a system is referred as consistent and independent. That is, only one set of values of the variables can satisfy both the equations.
Graphically, the ordered pair of the point of intersection of the straight lines representing the equations is the solution set of the equations.
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