Himpunan penyelesaian sistem persamaan 5x+3y=14 dan 3x-2y+3=0 adalah

5x + 3y = 14
3x - 2y +3 = 0 // 3x -2y = -3

5x + 3y = 14 (x2) 10x + 6y = 28
3x - 2y = -3 (x3) 9x -6y = -9 +
10x + 9x = 28 + (-9)
19x = 19
x = 1

subtitusi x
5x + 3y = 14
5.1 + 3 y = 14
3y = 14 - 5 = 9
y = 9/3 = 3

5x + 3y = 14......(pers.1)

3x - 2y + 3 = 0
3x - 2y = -3........(pers.2)

Eliminasi pers1 dan 2
10x + 6y = 28......(per.1 dikali 2)
9x - 6y = -9..........(pers.2 dikali 3)
__________ +
19x = 19
x = 19/19
x = 1

Substitusikan x = 1 ke pers1. atau 2
5x + 3y = 14
5 (1) + 3y = 14
5 + 3y = 14
3y = 14 - 5
3y = 9
y = 9/3
y = 3

Maka ,
(x, y) = (1,3)

Himpunan penyelesaian adl (x,y) = (1,3)