(A) Given equations are:$(1)$ $2x - y + 3 = 0$$(2)$ $y = 2x - \frac{3}{2}$Substitute the value of $y$ from equation $(2)$ into equation $(1)$:$2x - (2

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(A) Given equations are:$(1)$ $2x - y + 3 = 0$$(2)$ $y = 2x - \frac{3}{2}$Substitute the value of $y$ from equation $(2)$ into equation $(1)$:$2x - (2x - \frac{3}{2}) + 3 = 0$$2x - 2x + \frac{3}{2} + 3 = 0$$\frac{3}{2} + 3 = 0$$\frac{3 + 6}{2} = 0$$\frac{9}{2} = 0$Since $\frac{9}{2} \neq 0$,this statement is a contradiction.Therefore,the given pair of linear equations has no solution,which means the lines are parallel. The correct option is $A$.

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

Medium

Solve the following pair of linear equations by the method of substitution: $2x - y + 3 = 0$ and $y = 2x - \frac{3}{2}$.

A
$\varnothing$
B
$(10, 2)$
C
$(7, 9)$
D
$(4, 3)$

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Mix Examples - Pair of Linear Equations in Two Variables

Solve the following pair of equations by the method of cross multiplication:
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Medium

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For the pair of equations $\lambda x + 3y = -7$ and $2x + 6y = 14$ to have infinitely many solutions,the value of $\lambda$ should be $1$. Is the statement true? Give reasons.

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In the pair of equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if ............ then it has a unique solution.

Easy

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For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.

Medium

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Solve the following pair of linear equations by the method of substitution: $2x - y + 3 = 0$ and $y = 2x - \frac{3}{2}$.

Similar Questions

Solve the following pair of equations by the method of cross multiplication:$ax + by - a + b = 0$$bx - ay - a - b = 0$

In $\Delta ABC$,$m \angle A = x$,$m \angle B = 3x$,and $m \angle C = y$. If $3y - 5x = 30$,show that the triangle is right-angled and find the measures of all three angles.

For the pair of equations $\lambda x + 3y = -7$ and $2x + 6y = 14$ to have infinitely many solutions,the value of $\lambda$ should be $1$. Is the statement true? Give reasons.

In the pair of equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if ............ then it has a unique solution.

For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.

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Solve the following pair of equations by the method of cross multiplication:
$ax + by - a + b = 0$
$bx - ay - a - b = 0$