Determining a Number of Solutions Quick

Check

Determine whether the systems have one solution, no solution, or infinitely many solutions.

3x - 2y = 3; 6x - 4y = 1

One Solution

No Solution

Infinitely Many Solutions

3x - 5y = 8,5x - 3y = 2

3x + 2y = 8; 4x + 3y = 1

3x - y = 3; 2x - 4y = 2

3x - 4y = 2, 6x - y = 1

Intro

Done

No Solution

Step-by-step explanation:

For one solution;

it will be consistent and independent ( example, x = 1 and y = 2)

For no solution;

it will be inconsistent and independent ( example, 0 = 2)

For many solution;

it will be consistent and dependent ( example, 1 = 1,  2 = 2,  y = y,  x = x)

Given;

        3x - 2y = 3 equation (1)

        6x - 4y = 1 equation (2)

6:     18x - 12y = 18 equation (3)

3:     18x - 12y = 3 equation (4),      subtract (4) from (3)

        0 - 0      =  15

       0 = 15

The solution is inconsistent and independent, because zero (0) cannot be equal to 15

Thus, the system has no solution

ONE SOLUTION

3x-5y=8; 5x-3y=2

3x+2y=8; 4x+3y=1

NO SOLUTION

3x-4y=2; 6x-8y=1

3x-2y=3; 6x-4y=1

INFINITELY MANY SOLUTIONS

3x-6y=3; 2x-4y=2

Step-by-step explanation:

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step-by-step explanation:

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step-by-step explanation: