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Graph of a pair of linear equations in two variables \(a_{1}x+b_{1}y+c_{1}=0\) and \(a_{1}x+b_{1}y+c_{1}=0\) will coincide,if

\(\frac{a_{1}}{a_{2}}\neq\frac{b_{1}}{b_{2}}\)
\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)
\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}\)
none of these

The graph of pair of linear equations \(a_{1}x+b_{1}y+c_{1}=0\) and \(a_{2}x+b_{2}y+c_{2}=0\) will intersect exactly at one point only,if

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\)
\(\frac{a_{1}}{a_{2}}\neq\frac{b_{1}}{b_{2}}\)
\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}\)
\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)

The system of a pair of linear equations \(a_{1}x+b_{1}y+c_{1}\) and \(a_{1}x+b_{1}y+c_{1}\) is consistent and have infinitely many solutions if their graphs are

parallel
intersect at one point
coincident
intersecting at one point or infinitely many points

Two running tracks are represented by a pair of linear equations x-2y = 6 and 3x-6y= 18.Graphically they represent

two parallel lines.
two perpendicular lines.
two non-parallel lines and intersect at a point
coincident lines

Form the pair of linear equations and solve graphically the real life mathematical problem "12 students took part in a mathematical seminar,if number of girls is two less than the number of boys, then number of boys and number of girls who participate is

number of boys=10 and number of girls=8
number of boys= 9 and number of girls=7
number of boys=7 and number of girls=5
number of boys=5 and number of girls=7

Mathematics

Ten Standard

Test your understanding of this lesson Graphical solution of a pair of linear equations | Introduction:-

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