NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 9
NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 9
Question:
Use elimination method to find all possible solutions of the following pair of linear equations:
\( 2x + 3y = 8 \)
\( 4x + 6y = 7 \)
Given:
Equation (1): \( 2x + 3y = 8 \)
Equation (2): \( 4x + 6y = 7 \)
To Find:
All possible solutions of the given pair of linear equations using elimination method.
Formula:
The elimination method involves manipulating the equations to eliminate one variable, allowing us to solve for the other variable.
Solution:
Step 1: Write the given equations.
$$ \begin{aligned} &\text{Equation (1):} \quad 2x + 3y = 8 \\ &\text{Equation (2):} \quad 4x + 6y = 7 \end{aligned} $$Step 2: Multiply equation (1) by 2 to make the coefficients of \(x\) the same in both equations.
$$ 2 \times (2x + 3y) = 2 \times 8 \\ \Rightarrow 4x + 6y = 16 \quad \text{(Equation 3)} $$Step 3: Subtract equation (2) from equation (3) to eliminate \(x\) and \(y\).
$$ (4x + 6y) - (4x + 6y) = 16 - 7 \\ 0 = 9 $$Step 4: Interpret the result.
Since the result is \( 0 = 9 \), which is a contradiction, the given pair of equations has no solution. This means the lines represented by the equations are parallel and do not intersect.
Result:
There is no solution to the given pair of linear equations.
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