Answer:
system (1) ⇒ Infinitely Many Solutions
system (2) ⇒ One Solution ⇒ ( 8/7 , 0)
system (3) ⇒ Infinitely Many Solutions
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
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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)
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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