Solution: 4x+5y=9 ... (i) 8x+10y=18 ...(ii) 2(4x+5y)=18 divide by 2 4x+5y=9...(iii) Now (i) and (iii) are same equaitons,so we have infinite number of solutions ...

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Standard X

Mathematics

Formation of a Quadratic Equation From It's Roots

4 x+5 y=98 x+...

Question

Find the number of solutions for the following pair of equations: $4 x + 5 y = 9$ and $8 x + 10 y = 18$

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Solution

Given: $4 x + 5 y = 9$ and $8 x + 10 y = 18$
Here, $a_{1} = 4, b_{1} = 5, c_{1} = 9$ and $a_{2} = 8, b_{2} = 10, c_{2} = 18$
$∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ as
$\frac{4}{8} = \frac{5}{10} = \frac{9}{18}$
Hence, the given pair of linear equations have infinite number of solutions.

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Find the number of solutions for the following pair of equations: 4x+5y=9 and 8x+10y=18

Given: 4x+5y=9 and 8x+10y=18Here, a1=4,b1=5,c1=9 and a2=8,b2=10,c2=18∴a1a2=b1b2=c1c2 as48=510=918Hence, the given pair of linear equations have infinite number of solutions.

Find the number of solutions for the following pair of equations: $4 x + 5 y = 9$ and $8 x + 10 y = 18$