Show that the lines

Solution:

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

So, taking equation $x+7 y=23$

Substituting $x=2$ and $y=3$

Lhs = x + 7y

$=2+7(3)$

$=2+21$

$=23$

$=\mathrm{RHS}$

Now, taking equation $5 x+2 y=16$

Substituting $x=2$ and $y=3$

LHS = 5x + 2y

$=5(2)+2(3)$

$=10+6$

$=16$

$=\mathrm{RHS}$

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