The number of solutions for each system of two linear equations.
Zero
Solutions
One
Solution
Infinitely
Many
Solutions
2x + 2y = 3
4x + 4y = 6
7x + 5y = 8
7x + 2y = 8
-2x + 3y = 7
2x - 3y = -7

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

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step-by-step explanation:

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.