Question

Use the substitution method to determine the vertices of the triangle formed by the following lines:
(a) 10x - 2y = 10
(b) x + 2y = 1
(c) 18x + 3y = 51​

Answer 1

Answer:

Given linear equations are

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=77⇒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=714⇒y=2

Now, x+2y=8 [From (iii)]

⇒x+2(2)=8