Show that the lines x + 7y = 23 and 5x + 2y = a 16 intersect at the point (2, 3).

Suppose the given two lines intersect at a point P(2, 3). Then, (2, 3) satisfies each of the given equations.

So, taking equation x + 7y = 23


Substituting x = 2 and y = 3


Lhs = x + 7y


= 2 + 7(3)


= 2 + 21


= 23


= RHS


Now, taking equation 5x + 2y = 16


Substituting x = 2 and y = 3


LHS = 5x + 2y


= 5(2) + 2(3)


= 10 + 6


= 16


= RHS


In both the equations pair (2, 3) for (x, y) satisfies the given equations, therefore both lines pass through (2, 3).


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