Question

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

Answer 1

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).