Use the elimination method to find all possible solutions of the following pair of linear equations:
$2x + 3y = 8$ $...(1)$
$4x + 6y = 7$ $...(2)$
$2x + 3y = 8$ $...(1)$
$4x + 6y = 7$ $...(2)$
(D) Step $1$: Multiply Equation $(1)$ by $2$ and Equation $(2)$ by $1$ to make the coefficients of $x$ equal. Then we get the equations as:
$4x + 6y = 16$ $...(3)$
$4x + 6y = 7$ $...(4)$
Step $2$: Subtracting Equation $(4)$ from Equation $(3)$:
$(4x - 4x) + (6y - 6y) = 16 - 7$
i.e.,$0 = 9$,which is a false statement.
Therefore,the pair of linear equations has no solution.
$4x + 6y = 16$ $...(3)$
$4x + 6y = 7$ $...(4)$
Step $2$: Subtracting Equation $(4)$ from Equation $(3)$:
$(4x - 4x) + (6y - 6y) = 16 - 7$
i.e.,$0 = 9$,which is a false statement.
Therefore,the pair of linear equations has no solution.
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