Q2.

2: The process of adding or subtracting to remove a variable and simplify solving the system of equations is called (substitution, elimination).

Verified

Answer

The purpose of adding or subtracting to remove a variable and simplify solving the system of equations is called elimination.

1Step-1 – Taking an example to justify the statement

Let us consider the equations,

$\begin{array}{l} 2 x + 3 y = 5 \\ 3 x + 2 y = 5 \end{array}$

2Step-2 –Multiplying the first equation by 2 and second by 3

By doing the above operation, we have

$\begin{array}{l} 4 x + 6 y = 10 \\ 9 x + 6 y = 15 \end{array}$

3Step-3 –Subtracting the two equations

$\begin{matrix} 4 x - 9 y = 10 - 15 \\ - 5 x = - 5 \\ x = 1 \end{matrix}$

Substituting the value of $x$ , we get

$\begin{matrix} 2 x + 3 y = 5 \\ 2 (1) + 3 y = 5 \\ 2 + 3 y = 5 \\ 2 + 3 y = 5 \\ 3 y = 5 - 2 \\ 3 y = 3 \\ y = 3 \end{matrix}$

Therefore, we see that by using elimination we simplify the system of equation.