Notes On Application of Linear Equations - CBSE Class 8 Maths
A linear equation in one variable may have variables on both sides of the equation. While solving the linear equations Numbers and Variables can be transposed from one side of an equation to the other side of the equation. Transposition Method for solving Linear equation in one variable 1) Obtain the linear equation 2) Identify the variable (quantity) and constants. 3) Simplify the L.H.S and R.H.S to their simplest forms by removing brackets. 4) Transpose all terms containing variables on L.H.S and constant terms on R.H.S. 5) Simplify L.H.S and R.H.S in the simpleest form. 6) Solve the equation obtained in step 5 by dividing both sides by the coefficients  of the variable on L.H.S. Cross-Multiplication Method for solving Linear equation in one variable The process of multiplying the numerator on the left hand side with the denominator on the right hand side and multiplying the denominator on left hand side with the numerator on right hand side is called cross multiplication. And then equating both the products we get the linear equation. On solving it we get the value of variable for which L.H.S. = R.H.S. Then, it is an equation of the form. $\frac{\text{(px + q)}}{\text{(mx + n)}}$= $\frac{\text{a}}{\text{b}}$ where m, n, p, q, a, b are numbers and mx + n ≠ 0 ⇒ a(mx + n) = b(px + q) . Using Linear Equations we can solve word problems. Following steps to solve a word problems. 1) Read the problem carefully and find out what is given and what is unknown. 2) Represent the unknown quantity by x. 3) Frame an equation in x, as per the conditions given in the problem. 4) Solve for x. For solving a Non-Linear Equation we have to reduce the Non Linear Equation into a linear Equation

#### Summary

A linear equation in one variable may have variables on both sides of the equation. While solving the linear equations Numbers and Variables can be transposed from one side of an equation to the other side of the equation. Transposition Method for solving Linear equation in one variable 1) Obtain the linear equation 2) Identify the variable (quantity) and constants. 3) Simplify the L.H.S and R.H.S to their simplest forms by removing brackets. 4) Transpose all terms containing variables on L.H.S and constant terms on R.H.S. 5) Simplify L.H.S and R.H.S in the simpleest form. 6) Solve the equation obtained in step 5 by dividing both sides by the coefficients  of the variable on L.H.S. Cross-Multiplication Method for solving Linear equation in one variable The process of multiplying the numerator on the left hand side with the denominator on the right hand side and multiplying the denominator on left hand side with the numerator on right hand side is called cross multiplication. And then equating both the products we get the linear equation. On solving it we get the value of variable for which L.H.S. = R.H.S. Then, it is an equation of the form. $\frac{\text{(px + q)}}{\text{(mx + n)}}$= $\frac{\text{a}}{\text{b}}$ where m, n, p, q, a, b are numbers and mx + n ≠ 0 ⇒ a(mx + n) = b(px + q) . Using Linear Equations we can solve word problems. Following steps to solve a word problems. 1) Read the problem carefully and find out what is given and what is unknown. 2) Represent the unknown quantity by x. 3) Frame an equation in x, as per the conditions given in the problem. 4) Solve for x. For solving a Non-Linear Equation we have to reduce the Non Linear Equation into a linear Equation

Next