Solve the following equations by the graphical method 3x + y + 4 = 0 and 6x – 2y + 4 = 0. Pls tell me fast.......
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Solve the following equations by the graphical method 3x + y + 4 = 0 and 6x – 2y + 4 = 0. Pls tell me fast.......
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Step-by-step explanation:
Given equations are x –2y –6 = 0
3x – 6y = 0
Here a1 = 1, b1 = –2, c1 = –6
a2 = 3, b2 = –6, c2 = 0
\frac{a_{1}}{a_{2}}= \frac{1}{3},\frac{b_{1}}{b_{2}}= \frac{-2}{6}= \frac{1}{3},\frac{c_{1}}{c_{2}}= \frac{-6}{0}
Here \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}
Here the given pair of linear equations is parallel. Therefore it has no solution Hence given pair of linear equations is inconsistent.
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\sf \: 3x + y + 4= 0 \\ \\ [/tex]
[tex]\bf\implies \:y = - 3x - 4 \\ \\ [/tex]
➢ Pair of points of the given equation are shown in the below table.
[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 4 \\ \\ \sf - 1 & \sf - 1 \\ \\ \sf - 2 & \sf 2 \end{array}} \\ \end{gathered} \\ [/tex]
Now, Consider
[tex]\sf \: 6x - 2y + 4 = 0 \\ \\ [/tex]
[tex]\sf \: 2(3x - y + 2) = 0 \\ \\ [/tex]
[tex]\sf \: 3x - y + 2 = 0 \\ \\ [/tex]
[tex]\bf\implies \:y = 3x + 2 \\ \\ [/tex]
[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 2 \\ \\ \sf - 1 & \sf - 1 \\ \\ \sf 1 & \sf 5 \end{array}} \\ \end{gathered} \\ [/tex]
➢ Now draw a graph using the points.
➢ See the attachment graph.
Now, from graph, we concluded that given system of equations is consistent having unique solution and solution is given by
[tex]\bf\implies \:x = - 1 \: \: \: and \: \: \: y = - 1 \\ \\ [/tex]