Question

Represent the following system of equations graphically and conclude whether the system is consistent or inconsistent.

2x + 3y = 6

4x + 6y = 24

Answer 1

2x + 3y = 6

x	0	3
y	2	0

For x = 0,

2(a) + 3y = 6

3y = 6

`y = 6/3`

y = 2

For x = 3,

2x + 3y = 6

2(3) + 3y = 6

6 + 3y = 6

3y = 0

y = 0

Now 4x + 6y = 24

x	0	6
y	4	0

For x = 0,

4(0) + 6y = 24

6y = 24

y = 4

For x = 6,

4x + 6y = 24

4(6) + 6y = 24

24 + 6y = 24

6y = 0

y = 0

Since lines are parallel, the system of equations is inconsistent.