Question

solve 2x-3y=6 and x+y=13 graphically

Answer 1

EXPLANATION.

Graph of the equation.

⇒ 2x - 3y = 6. - - - - - (1).

⇒ x + y = 13. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ 2x - 3y = 6. - - - - - (1).

Put the value of x = 0 in equation, we get.

⇒ 2(0) - 3y = 6.

⇒ - 3y = 6.

⇒ - y = 2.

⇒ y = -2.

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

Put the value of y = 0 in equation, we get.

⇒ 2x - 3(0) = 6.

⇒ 2x = 6.

⇒ x = 3.

Their Co-ordinates = (3,0).

From equation (2), we get.

⇒ x + y = 13. - - - - - (2).

Put the value of x = 0 in equation, we get.

⇒ (0) + y = 13.

⇒ y = 13.

Their Co-ordinates = (0,13).

Put the value of y = 0 in equation, we get.

⇒ x + (0) = 13.

⇒ x = 13.

Their Co-ordinates = (13,0).

Both curves intersects at a point = (9,4).

Answer 2

graphically

Question

solve 2x-3y=6 and x+y=13 graphically

Answer

6unit

Given equations

2x−3y+6=0

2x+3y−18=0

From the graph the intersection point is (3,4) .

The point of intersection with y-axis are (0,2),(0,6).

The length of base of triangle with y-axis =4 units

Height =4units

$= \frac{1}{2} \times 3 \times 4 \\ = 6 \: unit$