Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumUse 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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Similar Questions
Form the pair of linear equations for the following problems and find their solution by the substitution method.
The coach of a cricket team buys $7$ bats and $6$ balls for ₹ $3800$. Later,she buys $3$ bats and $5$ balls for ₹ $1750$. Find the cost of each bat and each ball.
The coach of a cricket team buys $7$ bats and $6$ balls for ₹ $3800$. Later,she buys $3$ bats and $5$ balls for ₹ $1750$. Find the cost of each bat and each ball.
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View SolutionOn comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$
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View SolutionSolve the following pair of linear equations:
$(a-b)x + (a+b)y = a^2 - 2ab - b^2$
$(a+b)(x+y) = a^2 + b^2$
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$(a+b)(x+y) = a^2 + b^2$
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View SolutionGiven the linear equation $2x + 3y - 8 = 0$,write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.
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View SolutionThe coach of a cricket team buys $3$ bats and $6$ balls for ₹ $3900$. Later,she buys another bat and $3$ more balls of the same kind for ₹ $1300$. Represent this situation algebraically and geometrically.
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