(A) system of linear equations in two variables $x$ and $y$ is represented as a coordinate pair $(x, y)$.Given the equations $x = 4$ and $y = 5$,the v

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(A) system of linear equations in two variables $x$ and $y$ is represented as a coordinate pair $(x, y)$.Given the equations $x = 4$ and $y = 5$,the value of $x$ is fixed at $4$ and the value of $y$ is fixed at $5$.Therefore,the unique solution point where these two lines intersect is $(4, 5)$.Thus,the solution set is ${(4, 5)}$.

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

Medium

The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$

A
$\{(4,5)\}$
B
$\{(5,5)\}$
C
$\{(5,4)\}$
D
$\{(4,4)\}$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

Solve the following pair of linear equations: $\frac{8}{a} - \frac{9}{b} = 1$ and $\frac{10}{a} + \frac{6}{b} = 7$.

Medium

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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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Are the following pair of linear equations consistent? Justify your answer.
$\frac{3}{5} x - y = \frac{1}{2}$
$\frac{1}{5} x - 3 y = \frac{1}{6}$

Medium

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Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$

Easy

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Draw the graph of the pair of equations $2x + y = 4$ and $2x - y = 4$. Write the vertices of the triangle formed by these lines and the $y$-axis. Also,find the area of this triangle.

Difficult

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The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$

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Solve the following pair of linear equations: $\frac{8}{a} - \frac{9}{b} = 1$ and $\frac{10}{a} + \frac{6}{b} = 7$.

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.

Are the following pair of linear equations consistent? Justify your answer.$\frac{3}{5} x - y = \frac{1}{2}$$\frac{1}{5} x - 3 y = \frac{1}{6}$

Solve the following pair of equations by the cross-multiplication method:$\frac{x}{a} - \frac{y}{b} = 0$$ax + by = a^2 + b^2$

Draw the graph of the pair of equations $2x + y = 4$ and $2x - y = 4$. Write the vertices of the triangle formed by these lines and the $y$-axis. Also,find the area of this triangle.

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Are the following pair of linear equations consistent? Justify your answer.
$\frac{3}{5} x - y = \frac{1}{2}$
$\frac{1}{5} x - 3 y = \frac{1}{6}$

Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$