system (1) ⇒ Infinitely Many Solutions
system (2) ⇒ One Solution ⇒ ( 8/7 , 0)
system (3) ⇒ Infinitely Many Solutions
Step-by-step explanation:
A) The first system of two linear equations.
2x + 2y = 3 ⇒(1)
4x + 4y = 6 ⇒(2)
If we multiply equation (1) by 2, we will get equation (2)
So, the system in fact represents one equation.
So, The system has Infinitely Many Solutions
B) The second system of two linear equations.
7x + 5y = 8 ⇒(1)
7x + 2y = 8 ⇒(2)
By subtract (1) - (2) we will get:
5y - 2y = 0
3y = 0
y = 0
Substitute at (1)
7x + 0 = 8
x=8/7
So, The system has only One Solution ⇒( 8/7 , 0)
C) The last system of two linear equations.
-2x + 3y = 7
2x - 3y = -7
If we multiply equation (1) by -1, we will get equation (2)
So, the system in fact represents one equation.
So, The system has Infinitely Many Solutions