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The solution set of the pair of equations $x+y+1=0$ and $3x+3y+k=0$ is an infinite set. Then $k = \dots$

Examine graphically whether the pair of equations $2x + 4y = 9$ and $3x + 6y = \frac{27}{2}$ is consistent.

Determine,algebraically,the vertices of the triangle formed by the lines:
$3x - y = 3$
$2x - 3y = 2$
$x + 2y = 8$

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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.

Solve the following pair of linear equations in two variables using a graph: $x + y = 8$ and $x - y = 2$.

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