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Solving a system of equations. After manipulating them, he decides to add the two equations shown below together to eliminate the variable x. What property justifies this manipulation? 6x+5y=17 -6x+2y=4

Respuesta :

Answer:

Addition property justifies manipulation of  the equations.

Step-by-step explanation:

Given:

Two equations.

⇒ [tex]6x+5y=17[/tex]    ...equation (i)

⇒ [tex]-6x+2y=4[/tex]   ...equation (ii)

We have to identify the property  which justifies the manipulation.

Note:

The Linear Combination Method:

  • Adding (or subtracting) a multiple of one equation with the other equation, in such a way that either the x -terms or the y -terms cancel out.
  • Then solve for x (or y) and substitute back to get the other values.
  • Also known as the addition and the elimination method.

The above equation is following the linear combination method where x-values are added to find the y value.

Solving:

⇒ [tex]6x+5y=17[/tex]  ...(i)

⇒ [tex]-6x+2y=4[/tex] ...(ii)

⇒ Adding both the equations.

⇒ [tex]7y=21[/tex]

⇒ Dividing both sides with 7.

⇒ [tex]y=\frac{21}{7}[/tex]

⇒ [tex]y=3[/tex]

Addition property justifies manipulation of both the equations.

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