Question

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

Answer 1

Addition property justifies manipulation of the equations.

Explanation:

Given:

Two equations.

⇒
`6x+5y=17` ...equation (i)

⇒
`-6x+2y=4` ...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:

⇒
`6x+5y=17` ...(i)

⇒
`-6x+2y=4` ...(ii)

⇒ Adding both the equations.

⇒
`7y=21`

⇒ Dividing both sides with 7.

⇒
`y=(21)/(7)`

⇒
`y=3`

Addition property justifies manipulation of both the equations.