Determine graphically the co-ordinates of the vertices of the triangle, the equations of
whose sides are: y = x, 3y = x, a ty = 8 (3)
need full answer by step by step explanation
Answers
Step-by-step explanation:
Answer
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
