Simultaneous Linear Equations ICSE Class 9 Maths MCQ

simultaneous-linear-equations-icse-class-10-maths-quiz-mcq

Simultaneous Linear Equations have two equations each with two variables and we have to find out the value of both the variables by solving the two equations simultaneously. This Maths quiz is based on this particular concept. This online Maths quiz will have a few multiple-choice questions. You are advised to take a separate notebook to solve the given sums in this maths quiz.

However, before you attempt the quiz, you should know about the main concept of simultaneous linear equations.
‘Simultaneous linear equations’ is a new concept for the students of ICSE class 9. You have done ‘linear equation in one variable’ in previous years( in classes 7 and 8 ). There you have to find the value of any one variable by solving the given equation.

Definition

An equation of the form ax + by + c = 0 or ax + by = c, where a, b, c are real numbers and a and b are non zero numbers and x and y are variables, is called a simultaneous linear equation or a linear equation in two variables.

Methods of Solving Simultaneous Linear Equations

There are three methods of solving any sum with simultaneous linear equations. The methods have been stated below:

1. Substitution method

2. Elimination Method

3. Cross-multiplication Method

1.Steps for solving Simultaneous Linear Equations with Substitution Method

(i) Solve any one of the given equations to find out the value of one variable in terms of the other variable. For example, if one of the equations is x + 2y = 4, then x = 4 – 2y.

(ii) Substitute the value of the variable so obtained in the other equation. For example, if the 2nd equation is 2x – y = 1, then it will become 2( 4 – 2y ) – y = 1

(iii) Solve this equation as you solve a linear equation with one variable.

(iv) Put the value of the variable obtained in step (iii) into the equation obtained in step (i) to find the value of the other variable.

2. Steps for solving Simultaneous Linear Equations with Elimination Method

(i) Bring the two equations in the form ax + by + c = 0 or ax + by = c,

(ii) Make the coeffecients of any one varible equal. For example, if the two equations are

2x + 3y = 2 …(i) and

3x – 5y = 1 ….(ii) then,

multiply equation (i) with 3 and equation (ii) with 2, so that in both the equations the coeffecients of x becomes 6.

Alternatively, you can multiply equation (i) with 5 and equation (ii) with 3, so that in both the equations the coefficients of x become 15.

(iii) Eliminate the variable with the same coefficients by adding or subtracting the two equations.

(iv) Put the value of the variable obtained in step (iii) into any of the two equations to find out the value of another variable.

3.Steps for solving Simultaneous Linear Equations with Cross-multiplication Method

(i) Bring the two equations in the form ax + by + c = 0

(ii) Put the values of the coefficients of each equation in the formula given below:

(iii) Find the values of the variables.

Word Problems On Simultaneous Linear Equations

The syllabus also contains word problems on simultaneous linear equations. The online maths quiz with multiple choice questions also has few word problems on simultaneous linear equations.

Here, you have to make two equations with the information given in the sentences. After the two equations being obtained this way, you can use any of the three methods illustrated above to solve the equation.

If you want to know how to solve the sums on Simultaneous Linear Equations or A pair of Linear Equations In Two Variables ICSE Class 9 Maths, you can follow the link given below for video tutorial of the chapter. In this video series, all the methods along with the word problems have been explained.

Video tutorials: