# Linear Equations Class-8 RS Aggarwal ICSE Maths Goyal Brothers

**Linear Equations Class-8 RS** Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-15. We provide step by step Solutions of Exercise / lesson-15 **Linear Equations** for ICSE **Class-8 RS** Aggarwal Mathematics.

Our Solutions contain all type Questions of Exe-15 A, Exe-15 B, Exe-15 C (MCQ) with Notes to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

**Linear Equations Class-8 RS** Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-15

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**Notes on Linear Equations**

Linear Equations Class 8 Notes- Chapter 15- The solution to this linear equation can be any rational number. This equation may consist expressions which are linear on both sides of the equal to sign. Just like numbers, we can also transpose the variables from one side of the equation to the other side.

**Equation:**

An equation is a statement of equality which contains one or more unknown quantity/ quantities (or variable/variables) is called an equation.

**Solving an Equation:**

Solving an equation means determining its root i.e., determining (finding) the value of the variable which satisfies it.

### Stepwise procedure to solve a word problem.

- Read the given word problem carefully and identify what is given and what is required.
- Use letters x, y, z, etc. to represent the unknown quantity.
- Transform the statements of the problem into mathematical statements.
- Form the linear equation according to the given condition (s) of the problem.
- Solve the equation by the usual method.
- Check the solution for its validity.
- Reject if the solution is invalid

**Solving Equations having the Variable on Both Sides**

**
**We transpose the terms in such a manner that the terms containing the variables are on the LHS and constant numbers on RHS.

Then, simplifying both sides and dividing by a suitable number (if required), we can solve the equation.

Finally, check the validity of the solution obtained. Reject if the solution is invalid

**Reducing Equations to Simpler Form**

**
**We multiply both sides of the equation by the LCM of the denominators of the terms in the expressions occurring in the given equation.

We transpose properly so that all the variable terms come on LHS and constant terms on RHS.

Then, combining like terms on both sides of the equation and dividing both sides by a suitable number (if required), we can find out the required solution.

Finally, we check this solution for its validity. Reject if the solution is invalid

**Equations Reducible to Linear Form**

**
**Sometimes the given equation is not linear in form. By cross-multiplication and further simplification, it can be transformed into a linear equation in one variable. Then, it can be solved by the usual method.

**Exe-15 (A ) **

**Linear Equations Class-8 RS** Aggarwal ICSE Maths Goyal Brothers Prakashan

**Solve the following equation**

**Question 1**

4 x – 9 = 2 x + 7

**Question 2**

**5 y + 18 = 11 – 2y**

**Question 3**

**21 – 3(x-7) = x + 20**

**Question 4**

**3 (y-7) – 2 ……………**

**Question 5**

**3 (t-5) – 16 t = 12 -2 (t-3)**

**Question 6**

**……………….**

**……………………..**

**…………………….**

**Question 15**

**(z+3) (z-3) – z (z+5) = 6**

**Question 16 **

**y (2y + 3) – 2y(y – 5) = 26**

**Question 17**

**…………………..**

**Question 18**

**3/4 ……………………..**

**Exe-15 (B), **

**Linear Equations Class-8 RS** Aggarwal ICSE Maths Goyal Brothers Prakashan

**Question 1**

**17 is less than four time a number is11. Find the number.**

**Question 2**

**If 10 be added ………………. Find the number.**

**Question 3**

**…………………………**

**………………………**

**………………………**

**Question 9**

**A number when …………………. Find the number.**

**Question 10 **

**Four-fifths of a number ……………………… find the number.**

**Question 11**

**…………………….**

**…………………..**

**……………………**

**Question 19**

**The sum of …………………….. find the original number.**

**Question 20**

**What same number ………………… are in proportion ?**

**Question 21**

**……………………….**

**………………………**

**………………………**

**Question 29**

**A man is five …………………….. present ages.**

**Question 30**

**A man is twice ……………….. present ages.**

**Question 31**

**………………………**

**………………………**

**…………………….**

**Question 38**

**A boat …………………….. in still water.**

**Question 39**

**The length of each ……………………….. sides of the triangle.**

**Question 40**

**………………………..**

**………………………..**

**…………………………**

**Question 44**

**Divide 600 in two parts such that 40 % of one exceeds 60 % of the other by 120.**

**Question 45**

**A workman is paid …………………….. For how days did he remain abest ?**

**MCQ Exe-15 (C), **

**Linear Equations Class-8 RS** Aggarwal ICSE Maths Goyal Brothers Prakashan

**Choose the correct option in each of the ****following**

**Question 1**

**If …………………………**

**Question 2**

**…………………….**

**………………………**

**……………………**

**Question 11**

** the age of a ………………… daughter is **

**Question 12**

**……………………**

**…………………….**

**…………………..**

**Question 19**

**For aiming at …………………. the target.**

**Question 20**

**A total of ………………… coins is.**

–: End of** Linear Equations Class-8 RS** Aggarwal Solutions :–

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