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Determine the equivalent system for the given system of equations:

2x + 3y = 7
4x – 2y = 4

A.2x + 3y = 7
8x – 4y = 4

B.2x + 3y = 7
6x + y = 11

C.-2x – 3y = 7
4x - 2y = 4

D.2x + 3y = 7
6x + y = 4​

Respuesta :

gmany

Answer:

[tex]\large\boxed{B.\ \left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+3y=7&(1)\\4x-2y=4&(2)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+3y=7\\4x-2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad6x+y=11\qquad(3)\\\\\text{Make the system of equation with (1) and (3):}\\\\\left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right[/tex]

The equivalent system of equations for the given system of equations is

option (B)

[tex]2x+3y=7\\6x+y=11[/tex]

This is obtained by adding the given equations.

Equivalent system of equations:

  • Systems of equations that have the same solution are called equivalent systems.
  • Given a system of two equations, we can produce an equivalent system by replacing one equation with the sum of the two equations, or by replacing an equation with a multiple of itself.

Calculating the equivalent system for the given system of equations:

Given the system of equations as

[tex]2x+3y=7\\4x-2y=4[/tex]

Adding the two equations,

[tex]2x+3y+4x-2y=7+4\\6x+y=11[/tex]

Therefore, the system of equations

[tex]2x+3y=7\\6x+y=11[/tex]

are equivalent to the given set of equations.

Thus, option (B) is correct.

Learn more about the equivalent system of equations here:

https://brainly.com/question/13028509

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