the number of solutions for each system of two linear equations. Zero Solutions One Solution Infinitely Many

Question

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​

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Katherine 2 weeks 2021-09-08T15:13:45+00:00 1 Answer 0

Answers ( )

    0
    2021-09-08T15:15:05+00:00

    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

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