Question

graphical method 1) 2x+y=8, x+y=4​

Answer 1

SolutioN :

We have, Pair of Linear Equation.

$\tt \dagger \: \: \: \: \: 2x + y = 8. \: \: \: - (1)$

$\tt \dagger \: \: \: \: \: x + y = 4. \: \: \: - (2)$

$\rule{90}1$

✎ Let's Take some value of x.

♢ Taking Equation ( 1 )

$\tt : \implies 2x + y = 8.$

$\tt : \implies 2(1) + y = 8.$

$\tt : \implies y = 8 - 2$

$\tt : \implies y = 6.$

$\rule{90}1$

☛ When, x = 2.

$\tt : \implies 2x+ y = 8.$

$\tt : \implies 2(2) + y = 8.$

$\tt : \implies 4 + y = 8.$

$\tt : \implies y = 8 - 4$

$\tt : \implies y = 4.$

$\rule{90}1$

☛ When, x = 3.

$\tt : \implies 2x + y = 8.$

$\tt : \implies 2(3) + y = 8.$

$\tt : \implies 6 + y = 8.$

$\tt : \implies y = 8 - 6$

$\tt : \implies y = 2.$

$\rule{120}3$

♢ Taking Equation ( 2 )

$\tt \dagger \: \: \: \: \: x + y = 4.$

☛ When, x = 1.

$\tt : \implies 1 + y = 4.$

$\tt : \implies y = 3.$

$\rule{90}1$

☛ When, x = 2.

$\tt : \implies x + y = 4.$

$\tt : \implies 2 + y = 4.$

$\tt : \implies y = 4 - 2.$

$\tt : \implies y = 2.$

$\rule{90}1$

☛ When, x = 3.

$\tt : \implies x+ y = 4.$

$\tt : \implies 3 + y = 4.$

$\tt : \implies y = 4 - 3$

$\tt : \implies y = 1.$

$\rule{120}3$

✡ Let's collect Information ↓

$\begin{array}{| c | c | c | c | }\cline{1-4}\multicolumn{4}{|c|}{ {\dagger \: \: \: \: \: 2x + y =8. }}\\ \cline{1-4} x & 1 & 2 & 3 \\ \cline{1-4} y & 6 & 4 & 2 \\ \cline{1-4} \end{array}$

$\begin{array}{| c | c | c | c | }\cline{1-4}\multicolumn{4}{|c|}{ {\dagger \: \: \: \: \: x + y = 4. }} \\ \cline{1-4} x & 1 & 2 & 3 \\ \cline{1-4} y & 3 & 2 & 1 \\ \cline{1-4} \end{array}$

Answer 2

Let two equations be ,

2 x + y = 8 ... (1)

x + y = 4 ... (2)

Let's take eq (1) , 2 x + y = 8.

When x = 1 ,

⇒ 2 (1) + y = 8

⇒ y = 6

When x = 2 ,

⇒ 2 (2) + y = 8

⇒ y = 4

When x = 3 ,

⇒ 2 (3) + y = 8

⇒ y = 2

Now take points (1,6) , (2,4) , (3,2) [From eq (1)]

Let's take eq (2) , x + y = 4

When x = 1

⇒ y = 3

When x = 2 ,

⇒ y = 2

When x = 3 ,

⇒ y = 1

Now take points (1,3) , (2,2) , (3,1) [ From eq (2) ]

Plot all of these points in a graph.