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.
x + 5y = 7
x + 5y = 20
x + 5y = 7 …(1)
x + 5y = 20 …(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 ]
x + 5y = 7 x + 5y = 20
∴ x + 5y + (-7) = 0 ∴ x + 5y + (–20) = 0
Or 1 × x + 5 × y + (-7) = 0 or, 1 × x + 5 × y + (-20) = 0
Here a1 = 1, b1 = 5, c1 = -7 and a2 = 1, b2 = 5, c2 = -20
Comparing the ratio of 
, we get
, 
and 
Here 
. Therefore, it is not solvable. Lines will be parallel.
Now, plot the lines on graph,
x + 5y = 7 y = 
... equation (i)
Equation (i) will be plotted as line AB.
x + 5y = 20 y = 
... equation (ii)
Equation (ii) will be plotted as line CD.
We can also see clearly in the graph that two lines are not intersecting each other at any point.
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