If a-1-a-2- b-1-b-2- c-1-c-2-for the system of equations a-1x - b-1y - c-1 - 0- and a-2x - b-2y - c-2 - 0These represent coincident lines-The system of equations have infinite solutions-only -a- and -b-none of these-

The correct option is C only (a) and (b) If a_1/a_2 = b_1/b_2 = c_1/c_2, the system of equations are consistent , coincident lines and have infinite solutions ...

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Byju's Answer

Standard X

Mathematics

Comparing the Ratios of Coefficients of a Linear Equation

If a_1/a_2 = ...

Question

If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ for the system of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$

These represent coincident lines

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The system of equations have infinite solutions

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only (a) and (b)

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none of these

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Solution

The correct option is C
only (a) and (b)

If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ , the system of equations are consistent , coincident lines and have infinite solutions.

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If a1a2=b1b2=c1c2 for the system of equations a1x+b1y+c1=0 and a2x+b2y+c2=0

The correct option is C only (a) and (b) If a1a2=b1b2=c1c2, the system of equations are consistent , coincident lines and have infinite solutions.

If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ for the system of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$

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only (a) and (b)

If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ , the system of equations are consistent , coincident lines and have infinite solutions.