Question

Determine graphically the vertices of the triangle formed by lines 3x - y = 3, 2x – 3y = 2 and x + 2y = 8​

Answer 1

Answer:

3x−y=3 ___(i)

2x−3y=2 ___(ii)

x+2y=8 ___(iii)

Let the intersecting points of lines (i) and (ii) is A, and of lines (ii) and (iii) is B and that of lines (iii) and (i) is C.

The intersecting point of (ii) and (i) can be find out by solving (i) and (ii) for (x, y).

3x−y=3 [From (i)]

2x−3y=2 [From (ii)]

9x−3y=9 __(iv) [multiplying eqn. (i) by 3]

2x−3y=2 [from (ii)]

− + −

7x=7

[By subtracting (ii) from (iv)]

⇒x=

7

7

⇒x=1

Now, 3x−y=3 [From (i)]

⇒3(1)−y=3[x=1]

⇒−y=3−3

⇒−y=0

⇒y=0

So, intersecting point of eqns.(i) and (ii) is A(1,0).

Similarly, intersecting point B of eqns. (ii) and (iii) can be find out as follows:

2x−3y=2 [from (ii)]

x+2y=8 [from (iii)]

2x−3y=2 [From (ii)]

2x+4y=16 __(v) [By multiplying (iii) by 2]

− − −

−7y=−14

[Subtracting (v) from (ii)]

⇒y=

7

14

⇒y=2

Now, x+2y=8 [From (iii)]

⇒x+2(2)=8

⇒x=8−4

⇒x=4

So, the coordinates of B are (4,2)

Similarly, for intersecting point of C of eqns. (i) and (iii), we have

3x−y=3 [From (i)]

x+2y=8 [From (iii)]

Multiplying (i) by 2, we get

6x−2y=6 ___(vi)

x+2y=8 [From (iii)]

7x=14

[Adding (vi) and (iii)]

⇒x=

7

14

⇒x=2

Now, 3x−y=3 [from (i)]

⇒3(2)−y=3

⇒−y=3−6

−y=−3⇒y=3

So, point C is (2,3)

Hence, the vertices of ΔABC formed by given three linear equations are A(1,0),B(4,2) and C(2,3)