Question

4x+3y=4, 2x-5y=6 का ग्राफ कैसे बनेगा?​

Answer 1

4x+3y=4,

2x-5y=6

• उन्मूलन द्वारा हल करने के लिए, चर में से एक का गुणांक दोनों समीकरणों में समान होना चाहिए ताकि एक समीकरण दूसरे से घटाए जाने पर चर रद्द हो जाए।

4x+3y=4, 2x-5y=6

• 4x और 2x को समान बनाने के लिए, पहले समीकरण के प्रत्येक पक्ष को 2 से गुणा करें और दूसरे के प्रत्येक पक्ष पर सभी शब्दों को 4 से गुणा करें।

$2(4x) + 2(3y) = 2(4) \\ 4(2x) + 4( - 3y) = 4(6)$

• सरल कीजिए

$8x + 6y = 8 \\ 8x - 12y = 24$

$8x - 8x + 6y + 12y = 8 - 24$

$6y + 12y = 8 - 24$

$18y = 8 - 24$

$18y = - 16$

$y = \frac{ - 8}{9}$

$2x - 3( \frac{ - 8}{9} ) = 6$

$2x + \frac{8}{3} = 6$

$2x = \frac{10}{3}$

$x = \frac{5}{3}$

$x = \frac{5}{3} \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{ - 8}{9}$

Answer 2

Given Question :-

• Draw graph of 4x+3y=4, 2x-5y=6.

─━─━─━─━─━─━─━─━─━─━─━─━─

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

Gɪᴠᴇɴ :

Linear equation,

$➢ \begin{gathered}\bf\blue{4x\:+\:3y\:=\:4} \\ \end{gathered}$

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

$\begin{gathered}:\implies\:\:\tt{4x + 3\times{0}\:=\:4} \\ \end{gathered}:$

$\begin{gathered}:\implies\:\:\sf{4x\:+\:0\:=\:4} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\:1} \\ \end{gathered}$

❷ Substituting 'y = 4' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{4x\:+\:3 \times 4\:=\:4} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{4x\:+\:12\:=\:4} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{4x\:=\: - 8} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\: - 2} \\ \end{gathered}$

❸ Substituting 'y = 2' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{4x\:+\:3 \times 2\:=\:4} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{4x\:+\:6\:=\:4} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{4x\:\:=\: - 2} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\: - 0.5} \\ \end{gathered}$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 1 & \sf 0 \\ \\ \sf - 2 & \sf 4 \\ \\ \sf - 0.5 & \sf 2 \end{array}} \\ \end{gathered}$

─━─━─━─━─━─━─━─━─━─━─━─━─

Gɪᴠᴇɴ :

Linear equation,

$➢ \:  \begin{gathered}\bf\blue{2x\: - \:5y\:=\:6} \\ \end{gathered}$

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

$\begin{gathered}:\implies\:\:\sf{2x\: - \:5 \times 0\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf {2x\: - \:0\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\:3} \\ \end{gathered}$

❷ Substituting 'y = 2' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{2x\: - 5 \times 2\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{2x\: - 10\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{2x\:=\:16} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\:8} \\ \end{gathered}$

❸ Substituting 'y = - 2' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{2x\: - 5 \times ( - 2)\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{2x\: + 10\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{2x\:\:=\:6 - 10} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{2x\:=\: - 4} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\: - 2} \\ \end{gathered}$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 3 & \sf 0 \\ \\ \sf 8 & \sf 2 \\ \\ \sf - 2 & \sf - 2 \end{array}} \\ \end{gathered}$

─━─━─━─━─━─━─━─━─━─━─━─━─

$\red{ \tt \:  ⟼ ➢ \: \: See \: the \: attachment \: graph.}$

─━─━─━─━─━─━─━─━─━─━─━─━─