Question

I WILL GIVE BRAINLIEST

John was asked to solve the following system using multiplication and addition. He tried twice to come up with an equivalent set of equations. Analyze each of John's attempts. Tell whether the attempt is an accurate and equivalent system of equations. Describe, in complete sentences, which operations were completed in each system and tell why or why not they were accurate operations.

Original System of Equations:

7x - 3y = 4

2x - 4y = 1

Attempt #1:

28x - 12y = 16

-6x + 12y = -3

Attempt #2:

14x - 6y = 4

-14x + 28y = 1

Answer 1

Answer:

Attempt #1

The attempt is accurate and the system of equations are equivalent

Attempt #2

The attempt is not accurate and the system of equations are not equivalent

Step-by-step explanation:

For attempt #1, the operations completed are;

1) Multiplication of the first equation by the coefficient of y in the second equation which is multiplication by 4

2) Multiplication of the second equation by the opposite sign (negative) coefficient of y in the first equation which is multiplication by (-3)

The above steps are completed the have obtain the lowest common multiple for the coefficients of y in opposite sign in both equations such that the sum of both equations will give an equation that has only one variable, x, left

The sum and solution then becomes 22·x = 13, x = 13/22

For attempt #2, the operations completed are;

1) Multiplication of the first equation by the coefficient of x in the second equation which is multiplication by 2

2) Multiplication of the second equation by the opposite sign (negative) coefficient of x in the first equation which is multiplication by (-7)

However the right hand side of the second equation was left out and should be -14·x + 28·y = -7

The above steps are completed the have obtain the lowest common multiple for the coefficients of x in opposite sign in both equations such that the sum of both equations will give an equation that has only one variable, y, left

The correct sum and solution then becomes 22·y = 3, y = 3/22