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