Question

The table can be used to determine the solution of equations, 2x − 2y = 6 and 4x + 4y = 28.

A table with 6 columns and 2 rows. The first column, Original System has 2 x minus 2 y equals 6 and 4 x plus 4 y equals 28. The second column, Equivalent System, has 4 x minus 4 y equals 12 and 4 x plus 4 y equals 28. The third column, Sum of equations in Equivalent System, has 8 x equals 40. The fourth column, Solution to System, is blank. The fifth column, New System Using Sum, has 4 x plus 4 y equals 28 and 8 x equals 40. The sixth column, Solution to New System is blank.

Which solution can be used to fill in both blanks in the table?

(2, 5)

(5, 2)
(5, −8)
(−8, 5)

Answer 1

I'm terrible at explaining so here's a screenshot

- Ripper

Explanation:

Answer 2

`(5,2)`

Explanation:

`2x-2y=6\\4x+4y=28`

Column 1 :

`2x-2y=6..........(1)\\4x+4y=28........(2)`

Column 2 :

Eqn(1)
`*\ 2`

`4x-4y=12\\4x+4y=28`

Column 3 :

Add the equations.

`(4x+4x)-4y+4y=12+28\\8x=40`

Fourth column :

`8x=40\\x=(40)/(8)=5`

Fift column :

`4x+4y=28\\8x=40`

Sixth column :

Substitute
`x=5`.

`4* 5+4y=28\\4y=28-20\\4y=8\\y=2`

Hence solution is
`(5,2)`.