Question

Determine graphically the vertices of a triangle, the equations of whose sides are given below:2y-x = 8, 5y - x = 14,- x + y/2 =1/2

Answer 1

Step-by-step explanation:

We have

2y−x=8

5y−x=14

y−2x=1

Now,

2y−x=8

⇒2y=8=x

⇒x=2y−8

When $$Y = 2$, we have

x=2×2−8=−4

When y=4, we have

x=2×2−8=−4

When y=4,wehavex=2×4−8=0

Thus, we have the following table giving points on the line 2y−x=8

x −4 0

y 2 4

Now,

5y−x=14

⇒5y−14=x

⇒x=5y−14

When y=2, we have

x=5×2−14=1

When y=3, we have

x=5×−14=1

Thus, we have the following table giving points on the line 5y−x=14

x −4 1

y 2 3

We have

y−2x=1

⇒y−1=2x

⇒x=

2

y−1

When y=3, we have

x=

2

3−1

=1

When y=−1, We have

x=

2

−1−1

=1

Thus, we have the following table giving points on the line y−2x=1

x −1 1

y 1 3

Graph of the given equations:

Ref. image

From the graph of the lines represented by the given equations, we observe that the lines

Taken in pairs intersect each other at points A(−4,2),B(1,3) and C(2,5)

Hence, the vertices of the triangle are A(−4,2),B(1,3) and C(2,5),

for the given system of equations