Check whether the system of evauation …

x + y = 5 ...(1)
2x + 2y = 10 ...(2)
Here, a₁ = 1, b₁ = 1, c₁ = -5
a₂ = 2, b₂ = 2, c₂ = -10
We see that {tex}\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} = \frac{{{c_1}}}{{{c_2}}}{/tex}
Hence, the lines represented by the equations (1) and (2) are coincident.
Therefore, equations (1) and (2) have infinitely many common solutions, i.e., the given pair of linear equations is consistent.
Graphical Representation, we draw the graphs of the equations (1) and (2) by finding two solutions for each if the equations. These two solutions of the equations (1) and (2) are given below in table 1 and table 2 respectively.
For equation (1) x + y = 5 {tex}\Rightarrow{/tex} y = 5 - x
Table 1 of solutions

For equations (2) x + 2y = 10
{tex}\Rightarrow{/tex} 2y = 10 - 2x
{tex}\Rightarrow y = \frac{{10 - 2x}}{2} \Rightarrow{/tex} y = 5 - x
Table 2 of solutions

We plot the points A(0, 5) and B(5, 0) on a graph paper and join these points to form  the line AB representing the equation (1) as shown in the figure, Also, we plot the points C(1, 4) and D (2, 3) on the same graph paper and join these points to form the line CD representing the equation (2) as shown in the same figure.
 
In the figure we observe that the two lines AB and CD coincide.