Tentukan himpunan penyelesaian dari sistem persamaan berikut dengan metode substitusi. a. {x+y=2 {x-y=8 b. {2×-3y=6 { x-y=1 c. {x-2y=5 {x+y = 11 d. {3x - 2y = 5 {4x + 3y = 6

<p>a) x + y = 2<br>x - y = 8<br>Penyelesaian<br>x + y = 2<br>x = - y + 2</p><p>x - y = 8<br>-y + 2 - y = 8<br>-2y = 8-2<br>-2y = 6<br>y = -3</p><p>x + y = 2<br>x + (-3) = 2<br>x = 5</p><p>Jadi Himpunan penyelesaian = { ( 5 , -3 ) }</p><p><br>b) 2x - 3y = 6<br>x - y = 1<br>Penyelesaian<br>x - y = 1<br>x = y + 1</p><p>2x - 3y = 6<br>2 ( y+1) - 3y = 6<br>2y + 2 - 3y = 6<br>- y = 4<br>y = - 4</p><p>x - y = 1<br>x - ( -4) = 1<br>x = 1 -4<br>x = -3</p><p>Jadi Himpunan penyelesaiannya = { (-3 , -4)}</p><p><br>c)x -2y = 5<br>x + y= 11<br>Penyelesaian<br>x + y = 11<br>x = - y + 11</p><p>x - 2y = 5<br>-y + 11 - 2y = 5<br>- 3y = -6<br>y = 2</p><p>x + y = 11<br>x + 2 = 11<br>x = 9</p><p>Jadi Himpunan penyelesaiannya = { ( 9, 2 ) }</p><p><br>d) 3x - 2y = 5<br>4x + 3y = 6<br>Penyelesaian<br>3x - 2y = 5<br>3x = 2y + 5<br>x = 2/3 y + 5/3</p><p>&nbsp;</p><p>4x + 3y = 6<br>4(2/3 y + 5/3) + 3y = 6<br>8/3 y + 20/3 + 3y = 6 (kedua ruas dikali 3)<br>8y + 20 + 9y = 18<br>17y = 18 - 20</p><p>17y = -2<br>y = -2/17</p><p>&nbsp;</p><p>x = 2/3 y + 5/3</p><p>x = 2/3 (-2/17) + 5/3</p><p>x = -4/51 + 85/51</p><p>x = 81/51</p><p>x = 27/17</p><p>&nbsp;</p><p>Jadi, x = 27/17 dan y = -2/17.</p>