Question

show graphically that the system of equations
3x-y = 2, 9x-3y =6​

Answer 1

EXPLANATION.

Graph of the equation,

(1) = 3x - y = 2.

(2) = 9x - 3y = 6.

From equation (1) we get,

(1) = 3x - y = 2.

Put x = 0 in equation, we get.

⇒ 3(0) - y = 2.

⇒ - y = 2.

⇒ y = -2.

Their Co-ordinates = (0,-2).

Put y = 0 in equation, we get.

⇒ 3x - (0) = 2.

⇒ 3x = 2.

⇒ x = 2/3 = 0.667.

Their Co-ordinates = (0.667,0).

From equation (2),

(2) = 9x - 3y = 6.

Put x = 0 in equation, we get.

⇒ 9(0) - 3y = 6.

⇒ 0 - 3y = 6.

⇒ 3y = -6.

⇒ y = -2.

Their Co-ordinates = (0,-2)

Put y = 0 in equation, we get.

⇒ 9x - 3(0) = 6.

⇒ 9x = 6.

⇒ x = 6/9 = 0.667.

Their Co-ordinates = (0.667,0).

Both curves overlap each other.

Answer 2

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

show graphically that the system of equations :-

3x-y = 2, 9x-3y =6 is consistent.

$\huge \orange{AηsωeR} ✍$

Line :- 1

The equation of line is 3x - y = 2

First, we find coordinates of points, which are lies in the line, in both x-axis & y-axis, which represents the graph structure.

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

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

↝ For graph see the attachment, the line passed through A(1, 1l and B(0, -2)

━─━─━─━─━─━─━─━─━─━─━─━─━─

Line :- 2

The equation of line is 9x - 3y = 6

First, we find coordinates of points, which are lies in the line, in both x-axis & y-axis, which represents the graph structure.

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{cccc}\bf x & \bf y \\ \frac{\qquad \qquad \qquad \qquad}{} & \frac{\qquad \qquad \qquad \qquad}{} \\ \sf 2 & \sf 4 \\ \\ \sf 3 & \sf 7 \end{array}} \\ \end{gathered}$

↝ For graph see the attachment, the line passed through P(2, 4) and Q(3, 7).

━─━─━─━─━─━─━─━─━─━─━─━─━─

Thus, the graph of two equations are coincident.

This implies, system of equations is consistent having infinitely many solutions.