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Select All the correct answers. Select all the statements that are true for the following systems of equations. System A 2x - 3y = 4 4xy18 System B 3x - 4y = 5 y = 5x + 3 System C 2x-3y и 4 12x-3y 54 System C simplifies to 2x-3y 4 and 4x y 18 by dividing the second equation by three. O Systems A and C have the same solution D Systems A and B have different solutions. Systems B and C have the same solution All three systems have different solutions.​

Sagot :

Killmaster143

Answer:

hi

Step-by-step explanation:

Answer:

The true statements are:

the first statement: Systems A and C have the same solution

the fourth statement: System C simplifies to 2x - 3y = 4 and 4x - y = 18

the fifth statement: Systems A and B have different soltuoins.

Explanation:

1) The first statement: systems A and C have the same solutiotn: TRUE

The fourth statement proves that that the two systems are equivalent which means that both have the same solution.

2) The second statement: All three systems have different solutions: FALSE

The fourth statement proves that the systems A and C have same solution, so this second statement is false.

3) The third statement: Systems B and C have the same solution: FALSE

You can solve the two systems and will find the solutions are different

Solution of system B.

3x - 4y = 5

y = 5x + 3

replace y = 5x + 3 in the first equation => 3x - 4(5x + 3) = 5

=> 3x - 20x - 12 = 5

=> - 17x = 5 + 12

=> -17x = 17

=> x = - 17 / 17

=> x = - 1

y = 5x + 3 = 5(-1) + 3 = - 5 + 3 = - 2

=> solution x = -1 and y = -2

Solution of system C.

2x - 3y = 4

12x - 3y = 54

subtract

4) fourth statement: System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three: TRUE

Look:

Second equation of system C = 12x - 3y = 54

Divide by 3:

12x - 3y     54

----------- = -----

    3           3

Distributive property:

12x      3y      

------ - ----- = 18

  3        3

4x - y = 18, which is the same second equation of system A, so the system C simplifies to the same system A, which is 2x - 3y = 4 and 4x - y = 18.

5) The fifth statement: systems A and B have different solutions: TRUE

You can solve the two systems and will find the solutions are different

Solution of system A:

 2x - 3y =  4      

12x - 3y = 54           since it is equivalent to 4x - y =  18

-------------------

12x - 2x = 54 - 4      subtracting the first equation from the secon

10x = 50                  adding like terms

x = 5                        dividing by 10

From 2x - 3y = 4 => 3y = 2x - 4 = 2(5) - 4 = 10 - 4 = 6

=> y = 6 / 3 = 2

=> x = 5, y = 2

Solution of system B.

3x - 4y = 5

y = 5x + 3

replace y = 5x + 3 in the first equation => 3x - 4(5x + 3) = 5

=> 3x - 20x - 12 = 5

=> - 17x = 5 + 12

=> -17x = 17

=> x = - 17 / 17

=> x = - 1

Which is enough to prove that the two systems have different solutions.

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