Question

The number of solutions for each system of two linear equations.

Answer 1

Answer:

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