Solve the simultaneous equations 3 2x – y = 7 xy = 15 August 23, 2021 by Thành Đạt Solve the simultaneous equations 3 2x – y = 7 xy = 15
Answer: (5, 3 ) and (- [tex]\frac{3}{2}[/tex], – 10 ) Step-by-step explanation: Given the 2 equations 2x – y = 7 → (1) xy = 15 → (2) Rearrange (1) expressing y in terms of x , that is y = 2x – 7 → (3) Substitute y = 2x – 7 into (2) x(2x – 7) = 15 2x² – 7x = 15 ( subtract 15 from both sides ) 2x² – 7x – 15 = 0 ← in standard form (x – 5)(2x + 3) = 0 ← in factored form Equate each factor to zero and solve for x x – 5 = 0 ⇒ x = 5 2x + 3 = 0 ⇒ 2x = – 3 ⇒ x = – [tex]\frac{3}{2}[/tex] Substitute these values into (3) for corresponding values of y x = 5 : y = 2(5) – 7 = 10 – 7 = 3 ⇒ (5, 3 ) x = – [tex]\frac{3}{2}[/tex] : y = 2(- [tex]\frac{3}{2}[/tex] ) – 7 = – 3 – 7 = – 10 ⇒ (- [tex]\frac{3}{2}[/tex], – 10 ) Reply
Answer:
(5, 3 ) and (- [tex]\frac{3}{2}[/tex], – 10 )
Step-by-step explanation:
Given the 2 equations
2x – y = 7 → (1)
xy = 15 → (2)
Rearrange (1) expressing y in terms of x , that is
y = 2x – 7 → (3)
Substitute y = 2x – 7 into (2)
x(2x – 7) = 15
2x² – 7x = 15 ( subtract 15 from both sides )
2x² – 7x – 15 = 0 ← in standard form
(x – 5)(2x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x – 5 = 0 ⇒ x = 5
2x + 3 = 0 ⇒ 2x = – 3 ⇒ x = – [tex]\frac{3}{2}[/tex]
Substitute these values into (3) for corresponding values of y
x = 5 : y = 2(5) – 7 = 10 – 7 = 3 ⇒ (5, 3 )
x = – [tex]\frac{3}{2}[/tex] : y = 2(- [tex]\frac{3}{2}[/tex] ) – 7 = – 3 – 7 = – 10 ⇒ (- [tex]\frac{3}{2}[/tex], – 10 )