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What are the solutions to the simultaneous equations of 3xy -y squared equals 8 and x -2y equals 1?
The two equations are:
1) 3xy - y² = 8
2) x - 2y = 1
Make x the subject of (2):
x - 2y = 1 → x = 2y + 1
substitute for x in (1) and solve for y:
3xy - y² = 8
→ 3(2y + 1)y - y² = 8
→ 6y + 3y - y² - 8 = 0
→ 5y + 3y - 8 = 0
→ (5y + 8)(y - 1) = 0
→ 5y + 8 = 0 → y = -8/5
or y - 1 = 0 → y = 1
and substitute into 2 to find the corresponding x:
y = -8/5 → x = 2(-8/5) + 1 = -11/5
y = 1 → x = 2(1) + 1 = 3
→ the solutions are the ordered pairs (-11/5, -8/5) {or (-2.2, -1.6)} and (3, 1)
What else can I help you with?
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