(C) Given equations are $2x + y = 6$ $(1)$ and $x + \frac{1}{2}y = 4$ $(2)$.Multiply equation $(2)$ by $2$,we get $2x + y = 8$.Comparing the two equat

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(C) Given equations are $2x + y = 6$ $(1)$ and $x + \frac{1}{2}y = 4$ $(2)$.Multiply equation $(2)$ by $2$,we get $2x + y = 8$.Comparing the two equations:$2x + y = 6$$2x + y = 8$Here,the coefficients of $x$ and $y$ are the same,but the constants are different $(6 \neq 8)$.This represents two parallel lines.Therefore,the system has no solution.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

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The pair of equations $2x + y = 6$ and $x + \frac{1}{2}y = 4$ has.........

A
unique solution
B
two solutions
C
no solution
D
infinite solutions

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

For a pair of equations $2x + 3y = 1$ and $3x - 2y = 8$,in usual notations $a_{1}b_{2} - a_{2}b_{1} = \dots$

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The cost of $5$ pants and $8$ shirts is ₹ $3100$. If the cost of a pant is ₹ $x$ and a shirt is ₹ $y$,then the linear equation in two variables is:

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$(-1, 3)$ is not a solution of the equation $\ldots \ldots \ldots \ldots$

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Is the pair of equations $x+2y-3=0$ and $6y+3x-9=0$ consistent? Justify your answer.

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Solve the following pair of linear equations by the method of substitution: $2x - 3y = -11$ and $4x - 6y + 22 = 0$.

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The pair of equations $2x + y = 6$ and $x + \frac{1}{2}y = 4$ has.........

Similar Questions

For a pair of equations $2x + 3y = 1$ and $3x - 2y = 8$,in usual notations $a_{1}b_{2} - a_{2}b_{1} = \dots$

The cost of $5$ pants and $8$ shirts is ₹ $3100$. If the cost of a pant is ₹ $x$ and a shirt is ₹ $y$,then the linear equation in two variables is:

$(-1, 3)$ is not a solution of the equation $\ldots \ldots \ldots \ldots$

Is the pair of equations $x+2y-3=0$ and $6y+3x-9=0$ consistent? Justify your answer.

Solve the following pair of linear equations by the method of substitution: $2x - 3y = -11$ and $4x - 6y + 22 = 0$.

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