How To Solve Linear Equations What is a linear equation: An equation is a condition on a variable. A variable takes on different values; its value is not fixed. Variables are denoted usually by letter of alphabets, such as x, y , z , l , m , n , p etc. From variables we form expression. Linear equation in one variable: These are the type of equation which have unique (i.e, only one and one ) solution. For example: 2 x + 5 = 0 is a linear equation in one variable. Root of the equation is −52 Example 1: Convert the following equation in statement form. x-5=9 Solution :- 5 taken from x gives 9 Know More About Common Pythagorean Triples
So x = 9 + 5 = 14 Hence, x = 14 For verification of the statement, x-5=9 14 - 5 = 9 9 = 9 So left hand side value is equal to right hand side value. Hence the value of x determined is correct . You can try out some more examples from linear equations worksheets Linear equation in two variable: An equation which can be put in the form ax+by+c=0, where a, b, and c are real numbers, and a and b are not zero, is called linear equation in two variables. For example: 3 x + 4 y = 8 which is a equation in two variables. Summary :- A linear equation in two variable has infinitely many solutions.The graph of every linear equation in two variable is a straight line. Learn More On :- Finding Asymptotes
Every point on the graph of a linear equation in two variable is a solution of the linear equation. An equation of the type y = mx represents a line passing through the origin. How to Solve Linear EquationsBack to Top Below are the methods for solving linear equations in one variable: Method 1: Isolate the variable: In this method we will isolate the variable on one side and number on other sides. Steps and example for solving equation: Example 1: solve 2x + 3 =15 Solution 1: Given equation is: 2x + 3 = 15 Step 2: Subtract 3 from both side 2x + 3 - 3 = 15 - 3 2 x =12 Step3: Isolate the variable by dividing 2 to both side 2x2 = 122
x=6 Solution is 6 Method 2: Graph method for linear equation in two variable. The graph of every linear equation in two variables is a straight line. Every point on the graph of a linear equation is a two variables is a solution of the linear equation. moreover, every solution of the linear equation is a point on the graph of the linear equation Example 1: Solve graphically y + 2x =6 Solution 1: Given equation: y + 2x = 6
How To Graph Linear Equations Graphing Linear Equations is one of the most important concepts of algebra and proper understanding is necessary to be good with it. Get help from an algebra tutor online and learn about graphing linear equations, understand all the basic and advance concepts of equations and achieve quality help here. Below is an example of graphing linear equations with one variable for a better understanding: Example : ax + b = 0 is a linear equation in one variable. To represent a graph of linear equation in one variable , Consider the equation 2x + 4 = 0 2x = -4 x = −42 x = -2
Since this equation is independent of y, for all values of y, x = -2 Hence x = -2 is a line parallel to the y-axis at x = -2. Before learning on how to graph linear equations in one variable x = -2, let us understand the basics on how to graph linear equations. How to Graph Linear Equations How to graph linear equations Of y = mx + c Step1: Choose the convenient values of x and find the corresponding values of y Step 2: Prepare a table for different pairs of values of x and y Step 3: Draw the axes on a graph paper and chose a suitable sale. Step 4: Plot the ordered pairs fro the above table on the graph paper Step 5: Join these points by a straight line This straight line is the graph of y = mx + c Remark : In the equation y = mx + c, we say that (i) m is the slope of the line Read More On :- Find Asymptotes
(ii) c is the y = intercept of the line. Example : How to Graph Linear Equations of the line y = 2x + 3. Write down its (i) y-intercept (ii) slope. Solution : We have x = 1 → y = (2 x 1 = 3) = 5 x = - 2 → y = {2 x (-2) + 3} = - 1 Thus, we have the following table Plot the Points A(1, 5) and B( - 2, - 1) on a graph paper. Join AB and produce it. Then, AB is the required graph of the line y = 2x + 3 clearly, (i) y-intercept = 3 (ii) slope = 2
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