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

(5, 2)

Work: Multiply first equation by 2 to get 4x − 4y = 12. Add to 4x + 4y = 28 to get 8x = 40 → x = 5. Substitute into 4x + 4y = 28: 20 + 4y = 28 → y = 2.