{ 4 x - 3y = 15
8 x² - 27 y² =45
Isolate y for 4 x - 3y = 15
4 x - 3y = 15 ( add 3y to both sides ):
4x-3y +3y = 15 + 3y
4x = 15 + 3y
Divide both sides by 4 :
4x / 4 = 15 + 3y / 4
x = 15+3y / 4
Plug the solutions x = 15+3y / 4 into : 8 x² - 27 y²=45
8 ( 15+3y / 4 )² - 27 y² = 45
1/2 ( 3y+15)² - 27 y² = 45
Multiply by LCD = 2
9 ( y+5)² - 54 y² = 90
-45 y² + 90 y + 225 = 90
- 45 y² + 90 y = 225 - 90
-45 y² + 90 y = 135 = 0
-45 ( y + 1 ) ( y - 3 ) = 0
Using the zero factor principle:
Solve ( y + 1 ) = 0
y = - 1
Solve ( y - 3 ) = 0
y = 3
y = -1 and y = 3
Plug the solution y = -1 , y = 3 into : 4 x - 3 y = 15
4 x - 3 y = 15 for - 1 :
4 x - 3 ( - 1 ) = 15
4 x + 3 = 15
4 x = 15 - 3
4 x = 12
x = 12 / 4
x = 3
For 3 :
4 x - 3 y = 15
4 x - 3 ( 3 ) = 15
4 x - 9 = 15
4 x = 15 + 9
4 x = 24
x = 24 / 4
x = 6
Therefore the final solution :
y = 3 , x = 6
y = - 1 , x = 3
hope this helps!