$(A)$ Let the number of boys be $x$ and the number of girls be $y$.According to the problem,the total number of students is $6$,so $x + y = 6$.The num

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$(A)$ Let the number of boys be $x$ and the number of girls be $y$.According to the problem,the total number of students is $6$,so $x + y = 6$.The number of girls is $2$ less than the number of boys,so $y = x - 2$,which can be written as $x - y = 2$.Solving the system of equations:$1) x + y = 6$$2) x - y = 2$Adding the two equations: $(x + y) + (x - y) = 6 + 2 \rightarrow 2x = 8 \rightarrow x = 4$.Substituting $x = 4$ into the first equation: $4 + y = 6 \rightarrow y = 2$.Thus,there are $4$ boys and $2$ girls.

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

Medium

$6$ students of class $X$ took part in the Ramanujan Competitive Examination. The number of girl participants is $2$ less than the number of boy participants. Find the number of girls and the number of boys who took part in the examination using a graph.

A
Boys: $4$,Girls: $2$
B
Boys: $7$,Girls: $3$
C
Boys: $8$,Girls: $4$
D
Boys: $6$,Girls: $12$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

Use the method of elimination to find the solution of the following pair of linear equations: $\frac{x}{4} + \frac{y}{3} = 2, 4x + 3y = 25$.

Medium

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Find the value$(s)$ of $p$ for the pair of equations $2x + 3y - 5 = 0$ and $px - 6y - 8 = 0$ if the system has a unique solution.

Difficult

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For what value$(s)$ of $k$ does the pair of equations $kx + 3y = k - 3$ and $12x + ky = k$ have no solution?

Difficult

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There are some students in the two examination halls $A$ and $B$. To make the number of students equal in each hall,$10$ students are sent from $A$ to $B$. But if $20$ students are sent from $B$ to $A$,the number of students in $A$ becomes double the number of students in $B$. Find the number of students in the two halls.

Medium

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Solve the following pairs of equations by the method of elimination:
$5x - 3y = 1$
$2x + 5y = 19$

Easy

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$6$ students of class $X$ took part in the Ramanujan Competitive Examination. The number of girl participants is $2$ less than the number of boy participants. Find the number of girls and the number of boys who took part in the examination using a graph.

Similar Questions

Use the method of elimination to find the solution of the following pair of linear equations: $\frac{x}{4} + \frac{y}{3} = 2, 4x + 3y = 25$.

Find the value$(s)$ of $p$ for the pair of equations $2x + 3y - 5 = 0$ and $px - 6y - 8 = 0$ if the system has a unique solution.

For what value$(s)$ of $k$ does the pair of equations $kx + 3y = k - 3$ and $12x + ky = k$ have no solution?

Solve the following pairs of equations by the method of elimination:$5x - 3y = 1$$2x + 5y = 19$

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Solve the following pairs of equations by the method of elimination:
$5x - 3y = 1$
$2x + 5y = 19$