Question

How do you solve a system of equations by using the elimination method?

Answer 1

Elimination method:

The elimination method is used in the linear equation of two or more variables to eliminate one of the variable.

It helps to simplify equations and find values of variables.

Steps to solve a system of equations by using the elimination method:

• Write the given equation in standard form.
• Find the lowest common multiple for each of the equations.
• Multiply each of the given equations with the lowest common multiple.
• Add or subtract the resultant equations to find the value of one variable.
• Substitute the obtained value in any of the given equations to find the value of another variable.

For example.

Consider two linear equations of two variables, $\mathrm{x}+3\mathrm{y}-3=0$ and $2\mathrm{x}+4\mathrm{y}-2=0$.

Write the two equations in standard form :

$$\begin{gathered} \mathrm{x}+3\mathrm{y}=3...\left(1\right) \\ 2\mathrm{x}+4\mathrm{y}=2...\left(2\right) \end{gathered}$$

The lowest common multiple of both the equation is $2$

Multiply the value lowest common multiple with the equations $\left(1\right)$ :

$$\begin{gathered} 2\times \left(1\right)\Rightarrow 2\mathrm{x}+6\mathrm{y}=6 \\ 1\times \left(2\right)\Rightarrow 2\mathrm{x}+4\mathrm{y}=2 \end{gathered}$$

Subtract the above two equations, the value of $\mathrm{y}=2$ :

Substitute the value of $y$ in $\left(1\right)$:

$$\begin{gathered} \mathrm{x}+3\left(2\right)=3 \\ \Rightarrow \mathrm{x}+6=3 \\ \Rightarrow \mathrm{x}=3-6 \\ \Rightarrow \mathrm{x}=-3 \end{gathered}$$

Hence, these $5$ steps are used to solve a system of linear equations of two or more variables by using the elimination method.