Question

solve simultaneous equation graphically x -y =2;x+y=6 ​

Answer 1

Answer:

x=4 y=2

Step-by-step explanation:

If we write these equations in a standard form it will be like this:

y= x-2

y= -x+6

These are two linear equations and we know that these two lines have a similar point.

to find this point, we have to put these two graphs equal:

x-2=-x+6

x=4

Now, we have our "x", we should just replace it in one of our equation.

y=(4)-2

y=2

Here's the point:

(4 , 2)

Hope you got it.

Please choose my answer as the brainliest.

Answer 2

$\large\underline{\bold{Given \:Question - }}$

Solve equations graphically :-

• x - y = 2

• x + y = 6

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

• Consider, x - y = 2

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

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

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

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

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

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

Hᴇɴᴄᴇ,

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

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

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

➢ See the attachment graph (Blue line)

Now,

• Consider x + y = 6

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

$\begin{gathered}:\implies\:\:\sf{0\:+\:y\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{y\:=\:6} \\ \end{gathered}$

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

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

$\begin{gathered}:\implies\:\:\bf{x\:=\:6} \\ \end{gathered}$

Hᴇɴᴄᴇ,

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

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

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

➢ See the attachment graph (Red line).

Hence,

$\rm :\implies\: \boxed{ \bf \: The \: solution \: is \: x = 4 \: and \: y = 2}$

Basic Concept Used :-

• For a system of linear equations involving two variables (x and y), each linear equation can be represented as a line in the cartesian plane. Since a solution to the linear system must satisfy all of the equations, the solution set will be the intersection of these lines, which is either a line or a single point, or the empty set.

A linear equation in two variables when plotted on a graph defines a line. So, this means when a pair of linear equations is plotted, two lines are defined. Now, there are two lines in a plane These lines can:

• intersect each other,

• be parallel to each other, or

• coincide with each other.

The point(s) where the two lines intersect will give the solutions of the pair of linear equations, graphically.