Question

solve the following system of equations graphically X + 2 y is equals to 4 , 4 x + 3 y is equals to 10​

Answer 1

Given Question :-

Solve the following system of equations graphically

• x + 2y = 4

and

• 4x + 3y = 10

Answer :-

Answer :- Given

First linear equation is

• x + 2y = 4

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

$\begin{gathered}:\implies\:\:\sf{0\:+2\:y\:=\:4} \\ \end{gathered}$

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

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

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

$\begin{gathered}:\implies\:\:\bf{x\:=\:4} \\ \end{gathered}$

Hᴇɴᴄᴇ,

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

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

➢ Now draw a graph using the points (0 , 2) & (4 , 0)

➢ See the attachment graph. (Red color line)

Now,

• Consider Second linear equation

• 4x + 3y = 10

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

$\begin{gathered}:\implies\:\:\sf{4x\:+\:0\:=\:10} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\:2.5} \\ \end{gathered}$

Substituting 'x = 1' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{4\:+\:3 \: y\:=\:10} \\ \end{gathered}$

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

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 2.5 & \sf 0 \\ \\ \sf 1 & \sf 2 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (1 , 2) & (2.5 , 0)

➢ See the attachment graph. (Purple color line)

Hence,

• From graph we conclude, x = 1.6 and y = 1.2.