Q.2 For each of the following system of equation find whether it has unique solution, infinite number of solutions or no solutions. $3 x - 5 y - 20 = 0, 6 x - 10 y = 40$

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Solution

Step 1: Given equations
Understanding & Applying
The given system of equations may be written as
$3 x - 5 y - 20 = 0, 6 x - 10 y = 40$
The given system of equations is in the form
$a_{1} x + b_{1} y + c_{1} = 0 a_{2} x + b_{2} y + c_{2} = 0$
Step 2: Given values of coefficients
$v a l u e s o f a_{1} = 3, b_{1} = - 5, c_{1} = - 20 a_{2} = 6, b_{2} = - 10, c_{2} = - 40 W e h a v e \frac{a_{1}}{a_{2}} = \frac{3}{6}, \frac{b_{1}}{b_{2}} = \frac{- 5}{- 10}, \frac{c_{1}}{c_{2}} = \frac{- 20}{- 40} T h e r f o r e, \frac{a_{1}}{a_{2}} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{1}{2}, \frac{c_{1}}{c_{2}} = \frac{1}{2}$
Step 3: Result
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} i . e \frac{1}{2} = \frac{1}{2} = \frac{1}{2}$
Therefore the given system of equations is dependent and has infinite number of solutions.

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Q.2 For each of the following system of equation find whether it has unique solution, infinite number of solutions or no solutions.3x-5y-20=0,6x-10y=40

Q.2 For each of the following system of equation find whether it has unique solution, infinite number of solutions or no solutions. $3 x - 5 y - 20 = 0, 6 x - 10 y = 40$