Question

Draw the graph of the equations

4x – y – 8 = 0 and 2x – 3y + 6 = 0. Also determine the

coordinates of vertices of the triangle formed by these lines and

the x-axis. Shade the triangular region.​

Answer 1

Answer:

We have system of equation:

A:4x−5y+16=0−−−(1)

B:2x+y−6=0−−−−(2)

For A

x0−41

y16/504

For B

x031

y604

From solving equation (1) & (2), we get only one point (1,4) as

−7y+28=0⇒y=4

4x−5y+16=04x+2y−12=0−−+

,x=

2

6−y

=

2

2−4

=1

So, the vertices are (−4,0),(1,4) & (3,0)

solution

Answer 2

Solution:
Given equations are 4x – y – 8 = 0 and 2x - 3y + 6 = 0
Consider the equation of line 4x – y – 8 = 0
If x =0
⇒ 4(0) - y - 8= 0
⇒ 0- y - 8= 0
⇒ y= - 8
If y = 0
⇒ 4x - 0 -8= 0
⇒ 4x = 8
⇒x = 2
The coordinates are
x
0
2
y
- 8
0


Consider the equation of line 2x - 3y + 6 = 0
If x =0
⇒ 2(0) - 3y + 6= 0
⇒ 3y =6
⇒ y= 2
If y = 0
⇒ 2x - 3(0) + 6= 0
⇒ 2x = -6
⇒x = -3
The coordinates are
x
0
- 3
y
2
0