check graphical whether the pair of …

Graph of the equation {tex}x + 3y = 6{/tex}:
We have, {tex}x + 3y = 6{/tex} {tex} \Rightarrow {/tex} {tex}x = 6 - 3y{/tex}
When y = 1, we have x = 6 - 3 =3
When y = 2, we have x = 6 - 6 = 0
Thus, we have the following table:

Plotting the points {tex}A(3,1)\ and\ B(0,2){/tex} and drawing a line joining them, we get the graph of the equation x + 3y = 6 as shown in Fig.
Graph of the equation {tex}2x - 3y = 12{/tex} :
We have, {tex} 2 x - 3 y = 12 \Rightarrow y = \frac { 2 x - 12 } { 3 }{/tex}
When x=3, we have {tex}y = \frac { 2 \times 3 - 12 } { 3 } = - 2{/tex}

When x=0, we have {tex}y = \frac { 0 - 12 } { 3 } = - 4{/tex}

Plotting the points {tex}C(3,-2)\ and\ D(0, - 4){/tex} on the same graph paper and drawing a line joining them, we obtain the graph of the equation {tex}2x - 3y = 12{/tex} as shown in Fig.
Clearly, two lines intersect at P(6, 0).
Hence, {tex}x = 6, y = 0{/tex} is the solution of the given system of equations.
Putting x = 6, y = 0 in {tex}a = 4x + 3y{/tex}, we get
a = (4 {tex}\times{/tex} 6) + (3 {tex}\times{/tex} 0) = 24