# How to find the equation of the line which passes through the point of intersection of the lines 7x − 3y − 19 = 0 and 3x + 2y + 5 = 0, give that the line is parallel to the line with the equation y = 2x + 1?

Contd.

We will use the following well-known

the form

Result :

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Let equation of any straight line passing through the point of intersection of two given straight line be

#=>(7k+3)x+(2-3k)y+(5-19k)=0.. [1]#

then

Inserting the value of k in [1]

This is the equation of the required straight line.

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The first step is to find the point of intersection of the 2 lines.

That is we attempt to eliminate the x or y term from the equations leaving us with an equation in 1 variable which we can solve.

Labelling the equations.

That is the y terms have the same coefficient but with opposing signs. Hence summing them will result in their elimination.

Substitute this value into either of ( 1 ) or ( 2 ) and solve for y

Substitute these values into ( 1 )

distribute and simplify.

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First, we need to find the point of intersection of the given lines. We solve the system of equations formed by the two lines:

7x - 3y - 19 = 0 3x + 2y + 5 = 0

By solving this system, we find the coordinates of the point of intersection.

Once we have the coordinates of the point of intersection, we can use the fact that the line we're looking for is parallel to the line with the equation y = 2x + 1. Since parallel lines have the same slope, we know that the slope of the line we're looking for is also 2.

Now, we can use the point-slope form of a linear equation, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

Substituting the coordinates of the point of intersection and the slope into the point-slope form, we can find the equation of the line.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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