Diketahui sistem persamaan linear dua variabel 2x+ 3y = 11 dan 3x - 2y = -3. Himpunan penyelesaian dari sistem persamaan irear tersebut adalah.... a. {(1,2)) b. {(1,3)} c. {(2,1)) d. ((3.1))
Penyelesaian
2x + 3y = 11
3x - 2y = -3
[tex](2x + 3y) \times 3 = 11 \times 3[/tex]
[tex](3x - 2y) \times 2 = -3 \times 2[/tex]
6x + 9y = 33
6x - 4y = -6
= 6x + 9y) - (6x - 4y)
= 33 - (-6)
= 9y + 4y
= 33 + 6
13y = 39
[tex]y = \frac{39}{13}[/tex]
y = 3
2x + 3(3) = 11
2x + 9 = 11
2x = 11 - 9
2x = 2
[tex]x = \frac{2}{2}[/tex]
x = 1
HP = (1,3)
Nilai y
[tex]2x + 3y = 11 | \times 3 \\ 3x - 2y = - 3 | \times 2 \\ \\ 6x + 9y = \: \: 33 \\ 6x - 4y = - 6 \\ ........................ - \\ \: \: \: \: \: \: \: \: \: \: 13y = 39 \\ \: \: \: \: \: \: \: \: \: \: \: \: y = 3 \\ \\ Nilai \: x \\ 2x + 3y = 11 \\ \: \: \: \: \: \: \: \: \: \: \:3y = \: \: 9 \\ ...................... - \\ 2x \: \: \: \: \: \: \: \: \: \: = \: \: 2 \\ x = 1[/tex]
HP = {( 1 , 3 )} ( b )