Question

Find the solution of the following pair of linear
equations by the graphical method.
2x+y=10 , x+y=6​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

Consider Line (1)

$\rm :\implies\: \boxed{ \pink{ \bf \: 2x \: + y \: = \tt \: 10}}$

❶ Substituting 'x = 0' in the given equation, we get

$\rm :\implies\:2 \times 0 + y = 10$

$\rm :\implies\:y \: = \: 10$

❷ Substituting 'y = 0' in the given equation, we get

$\rm :\implies\:2x + 0 = 10$

$\rm :\implies\:2x = 10$

$\rm :\implies\:x = 5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 10 \\ \\ \sf 5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 10) & (5 , 0)

➢ See the attachment. Red line represents 2x + y = 10

Now,

Consider Line (2)

$\rm :\implies\: \boxed{ \pink{ \bf \: x \: + \: y \: = \tt \: 6}}$

❶ Substituting 'x = 0' in the given equation, we get

$\rm :\implies\:0 + y = 6$

$\rm :\implies\:y \: = \: 6$

❷ Substituting 'y = 0' in the given equation, we get

$\rm :\implies\:x + 0 = 6$

$\rm :\implies\:x \: = \: 6$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6 \\ \\ \sf 6 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 6) & (6 , 0)

➢ See the attachment. Purple line represents x + y = 6.

$\rm :\implies\: \boxed{ \pink{ \bf \: Hence \: the \: solution \: is \: = \tt \: (4, 2)}}$

So,

$\rm :\implies\: \boxed{ \green{ \bf \: x = 4 \: \: and \: \: y \: = \: 2\: }}$

Answer 2

Step-by-step explanation:

this much only solve using graph method