Find the equation of the line that passes through the point of intersection of x + 2y = 9 and 4x -2y = -4 and the point of intersection of intersection of the lines 3x - 4y = 14 and 3x + 7y = -8.

Step-by-step explanation:

The point of intersection of

and

is the solution of the two equations.

We add equation (1) and equation(2) to get,

We put into equation (1) to get,

Therefore the line passes through the point, .

The line also passes through the point of intersection of

and

We subtract equation (3) from equation (4) to obtain,

We substitute this value into equation (4) to get,

The line also passes through

The slope of the line is

The equation of the line is

is the required equation

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