• LINEAR EQUATION• FORM OF LINEAR EQUATION• TYPES OF LINEAR EQUATION• GRAPH OF A EQUATION• TYPES OF GRAPH• HOW CAN KNOW ABOUT GRAPH?• EXAMPLES OF TYPES OF GRAPH• FORMULA OF CROSS – MULTIPLICATION• SOLVE QUESTION
LINEAR EQUATIONLinear equations are functions which have two variables. They have an independent and dependent variable.Independent Variables Dependent VariablesIndependent variables Dependent variablesare variables that you are variables that youput into the equations solve for
The general form for a pair of linear equation in two variables of x and y is -> a1 + b1 +c1 = 0 a2 + b2 + c2 = 0Where a1,b1,c1,a2,b2,c2 are real numbers and a, and b both are not zero.
What is linear equation in two variable?Equations of the form ax + by = c are called linear equations in two variables.How many types of method to find the solution of pair of linear equation?There are of four types1. Elimination method2. Substitution method3. Cross-multiplication method4. Graph method
Linear equation graph yThis is the graph of theequation 2x + 3y = 12. x -2 2The point (0,4) is the y-intercept.The point (6,0) is the x-intercept.
The graph of a pair of variable is represnted by two lines• If the line intersect at a point, then that point gives a unique solution and the pair of equation is consistent.• If the line is coincide, then there are infinite many solution and the pair of equation is consistent• If the line are parallel, then there are no solution and the pair of equation is inconsistent.
a1 ≠ b1 so the pair of linear equation is unique.a2 b2a1=b1 ≠c1 so the pair of linear equation is noa2 b2 c2 solution.a1=b1= c1 so the pair of linear equation is infinitya2 b2 c2 many solution
Two lines are parallel if If a1=b1 ≠c1 so the lines will be parallel. a2 b2 c2 (0, 4) Example: The lines 2x – y = 3 and 2x –y = -4 2 = -1 ≠ 3 2 -1 -4 (0, -3)The lines are parallel.
Two lines are coincident if If a1=b1 =c1 so the lines will be coincident. a2 b2 c2Example: .The lines 9x + 3y = -12 (-2,2)and18x + 6y = -249 = 3 ≠ -12 (-1,-1)18 6 -24 0,-4) The lines are coincident.
Two lines are intersect if If a1=b1 =c1 so the lines will be intersect. a2 b2 c2 (0,5) Example: The lines 2x + y = 5 (2,1) and 2x –2y = 2 (0,1) 2≠1 2 -2The lines are Intersect.
How to solve equation by cross multiplication method? Method to solve equation by cross multiplication in linear equation in two variable.x = b1c2 – c1b2 y = c1a2 – a1c2 a1b2 – b1a2 a1b2 – b1a2