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).