In our notes for Class 8, we had learned about linear equations and simultaneous linear equations. We suggest that you quickly revise the basic concepts of linear equations and how to solve two such equations simultaneously.

\displaystyle \textbf{Linear Equation in Two Variables}
\displaystyle \text{An equation of the form }ax+by+c=0,\text{ where }a,\ b\text{ and }c\text{ are real numbers}
\displaystyle (a\ne0,\ b\ne0),\text{ is called a linear equation in two variables }x\text{ and }y.
\displaystyle \text{Such an equation has degree }1.

\displaystyle \text{Two linear equations in two variables }x\text{ and }y\text{ are said to form a system of}
\displaystyle \text{simultaneous linear equations if each of them is satisfied by the same pair of values}
\displaystyle \text{of }x\text{ and }y.

\displaystyle \text{You learned about the Substitution Method and Elimination Method for solving}
\displaystyle \text{two linear equations simultaneously in Class 8.}

\displaystyle \text{There is another method called the Cross Multiplication Method by which we can solve}
\displaystyle \text{simultaneous linear equations. Let}
\displaystyle a_1x+b_1y+c_1=0
\displaystyle a_2x+b_2y+c_2=0
\displaystyle \text{be a system of simultaneous linear equations in two variables }x\text{ and }y\text{ such that}
\displaystyle \frac{a_1}{a_2}\ne\frac{b_1}{b_2},\text{ i.e. }a_1b_2-a_2b_1\ne0.
\displaystyle \text{Then the system has a unique solution given by}
\displaystyle x=\frac{b_1c_2-b_2c_1}{a_1b_2-a_2b_1}\qquad\text{and}\qquad y=\frac{c_1a_2-c_2a_1}{a_1b_2-a_2b_1}

\displaystyle \text{You may use the Substitution Method, Elimination Method or Cross Multiplication}
\displaystyle \text{Method to solve simultaneous linear equations. Regular practice will help you become}
\displaystyle \text{comfortable with each method.}

\displaystyle \textbf{Points to Remember}
\displaystyle \textbf{1. Linear Equation:}
\displaystyle \text{An equation which involves only one variable with highest power }1\text{ is called a} \\ \text{linear equation.}

\displaystyle \textbf{2. Solving the Equation}
\displaystyle \text{To solve an equation means to find the value of the variable which satisfies the equation.}

\displaystyle \textbf{3. Rules for Solving a Linear Equation:}
\displaystyle \text{The equality of a linear equation is not changed when:}
\displaystyle \text{(i) The same number is added to or subtracted from both sides of the equation.}
\displaystyle \text{(ii) Both sides of the equation are multiplied or divided by the same non-zero number.}

\displaystyle \textbf{4. Transposition:}
\displaystyle \text{When any term of the equation is taken from one side to the other, this process is} \\ \text{called transposition.}

\displaystyle \textbf{5. Cross Multiplication:}
\displaystyle \text{If }\frac{a}{b}=\frac{c}{d}\text{, then }a\times d=b\times c.
\displaystyle \text{This process is called cross multiplication.}

\displaystyle \textbf{6. Word Problems:}
\displaystyle \text{Word problems can be solved by means of equations by representing the unknown} \\ \text{quantity as }x,\;y,\;z\text{ etc.,}
\displaystyle \text{and then solving the equation formed according to the condition or conditions given} \\ \text{in the problem.}

Discover more from ICSE / ISC / CBSE Mathematics Portal for K12 Students

Subscribe to get the latest posts sent to your email.