What is the best approximation of the solution to the system to the nearest integer values? 2x-5y=-20

3x+2y=20

2x - 5y = - 20 ⇒ 4x - 10y = - 40

3x + 2y = 20 ⇒ 15x + 10y = 100

19x = 60

19 19

x = 3³/₁₉

2x - 5y = - 20

2 (3³/₁₉) - 5y = - 20

6⁶/₁₉ - 5y = - 20

- 6⁶/₁₉ - 6⁶/₁₉

-5y = - 26⁶/₁₉

-5 - 5

y = 5⁵/₁₉

(x, y) = (3³/₁₉, 5⁵/₁₉)

The best approximation of the solution to the system of the nearest integer values are (4, 6), or (x, y) ≈ (4, 6).