mohamedkassime12
Answered

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Which system of equations has the same solutions as the system below?
3x -y =7
2x + 3y = 12


(1) 6x -2y = 14
-6x + 9y = 36

(2) 18x - 6y = 42
4x + 6y = 24

(3)-9x - 3y = -21
2x + 3y = 12

(4) 3x - y = 7
x +y = 2​

Sagot :

Answer:

(2) 18x - 6y = 42

4x + 6y = 24

Step-by-step explanation:

3x -y =7

2x + 3y = 12

This system has solution x=3; y =2.

And also the system (2). So (2) it's the correct answer.

For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is B.

What is a System of equations?

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

The solution for the given system of equation is,

3x-y=7

y = 3x - 7

2x+3(3x-7)=12

2x + 9x - 21 = 12

11x = 33

x = 3

y = 2

The system of the equations which satisfies when the value of x=3 and y =2 is substituted will have the same solution as the above system.

A.) 6x -2y = 14

    -6x + 9y = 36

  • 6(3) - 2(2) = 14

        18 - 4 = 14

  • -6(3) + 9(2)

        -18 + 18 = 0

B.) 18x - 6y = 42

    4x + 6y = 24

  • 18(3) - 6(2) = 42

        54 - 12 = 42

  • 4(3) + 6(2) = 24

        12+12 = 24

Since, both the equation are satisfied this is our solution.

Hence, the correct option is B.

Learn more about System of the equation:

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