Two equations in the variables $x$ and $y$ written in the standard form where
$a_{1} x + b_{1} y + c_{1} = 0 a n d$
$a_{2} x + b_{2} y + c_{2} = 0$ ,
have the coefficients as follows:
$a_{1} = 5, b_{1} = 6, c_{1} = 4, a_{2} = 10, b_{2} = 12, c_{2} = 7$ .
What is the nature of these two lines?

Coincident

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Intersecting

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Parallel

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Coincident or parallel

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Solution

The correct option is C
Parallel

The equations of the two lines are:
$5 x + 6 y + 4 = 0$
$10 x + 12 y + 7 = 0$
When we plot the graphs of these two equations, it is visible that they are parallel to each other.

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Two equations in the variables x and y written in the standard form where a1x+b1y+c1=0 and a2x+b2y+c2=0, have the coefficients as follows: a1=5,b1=6,c1=4,a2=10,b2=12,c2=7. What is the nature of these two lines?

The correct option is C Parallel The equations of the two lines are: 5x+6y+4=0 10x+12y+7=0 When we plot the graphs of these two equations, it is visible that they are parallel to each other.

Two equations in the variables $x$ and $y$ written in the standard form where
$a_{1} x + b_{1} y + c_{1} = 0 a n d$
$a_{2} x + b_{2} y + c_{2} = 0$ ,
have the coefficients as follows:
$a_{1} = 5, b_{1} = 6, c_{1} = 4, a_{2} = 10, b_{2} = 12, c_{2} = 7$ .
What is the nature of these two lines?

The correct option is C
Parallel

The equations of the two lines are:
$5 x + 6 y + 4 = 0$
$10 x + 12 y + 7 = 0$
When we plot the graphs of these two equations, it is visible that they are parallel to each other.