Class 10 Maths MCQs

Chapter 3 : Pair of Linear Equations in Two Variables

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1. If in equations $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0, \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$, then which of the following is true?

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2. The values of $x$ and $y$ from the equations $2 x-y=3$ and $4 x+y=3$ are:

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3. The graph of $x=5$ is:

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4. The given pair of equations $3 x-y=3$ and $9 x-3 y=9$ has:

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5. The larger angle is $24^{\circ}$ more than the smaller one in two supplementary angles. The value of angles are:

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6. For what value of $k$, the following equations have a unique solution:
$$ 2 x+k y=1 \text { and } 5 x-7 y=5 $$

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7. The values of $x$ and $y$ from the equations $x+y=14$ and $x-y=4$ are:

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8. If in equations $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0, \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$, then which of the following is true?

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9. The ratio of two numbers is $5: 7$ and sum is 360 , then the larger number will be:

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10. One number is 5 more than another number. If the sum of numbers is 75 , then the smaller number will be:

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11. The lines of graphical representation of the pair of equations $2 x-3 y+9=0$ and $4 x-6 y$ $+18=0$ will be:

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12. If in equations $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0, \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$, then which of the following is true?

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13. The denominator of a rational number is greater than its numerator by 5 . If 2 is subtracted from denominator and numerator each, then number becomes $\frac{2}{7}$. The rational number will be

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14. The sum of opposite angles of a cyclic quadrilateral is:

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15. The values of $x$ and $y$ from the equations $3 x+4 y=10$ and $x-y=1$ are:

Pair of Linear Equations in Two Variables Chapter 3 class 10 Basic Concepts

1. Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is
$$ \begin{aligned} & a_{1} x+b_{1} y+c_{1}=0 \\
& a_{2} x+b_{2} y+c_{2}=0
\end{aligned} $$ where $a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2}$ are real numbers, such that $a_{1}^{2}+b_{1}^{2} \neq 0, a_{2}^{2}+b_{2}^{2} \neq 0$.


2. Graphical Method to solve a pair of linear equations in two varibale:

The graph of a pair of linear equations in two variables is represented by two lines.

(i) If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent.

(ii) If the lines coincide, then there are infinitely many solutions - each point on the line being a solution. In this case, the pair of equations is dependent (consistent).

(iii) If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent.


3. If a pair of linear equations is given by $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$, then the following situations can arise :

(i) $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{1}}:$ In this case, the pair of linear equations is consistent.

(ii) $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}:$ In this case, the pair of linear equations is inconsistent.

(iii) $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ : In this case, the pair of linear equations is dependent and consistent.