By comparing the co-efficient of the same variables and constants of the following pairs of equations, let us write whether the pair of equations is solvable or not and check them by drawing the graphs of the equations.
5x + 8y = 14
15x + 24y = 42
5x + 8y = 14 …(1)
15x + 24y = 42 …(2)
Let us express the equations (1) and (2) in the form of
ax + by +c = 0 where a and b can’t be 0 at the same time.
[In the first equation, we use a1, b1, c1 and in second equation, we use a2, b2, c2 ]
5x + 8y = 14 15x + 24y = 42
∴ 5x + 8y – 14 = 0 ∴ 15x + 24y – 42 = 0
Or 5 × x + 8 × y + (-14) = 0 or, 15 × x + 24 × y + (-42) = 0
Here a1 = 5, b1 = 8, c1 = -14 and a2 = 15, b2 = 24, c2 = -42
Comparing the ratio of 
, we get
, 
and 
Here 
. Therefore, it is solvable and has infinite common solutions. Lines will overlap.
Now, plot the lines on graph,
5x + 8y = 14 y = 
... equation (i)
Equation (i) will be plotted as line AB.
15x + 24y = 42 y = 
... equation (ii)
Equation (ii) will be plotted as line CD.
Here in the graph also, we can see that both lines are overlapped on each other. Therefore it has infinite common solutions.
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