Solve the simultaneous equations. You must show all your working.
y = 4-X
x² + 2y2 = 67
x=
y=
X=

(7, - 3 ) and (- , )

Step-by-step explanation:

Given the 2 equations

y = 4 - x → (1)

x² + 2y² = 67 → (2)

Substitute y = 4 - x into (2)

x² + 2(4 - x)² = 67 ← expand and simplify left side

x² + 2(16 - 8x + x²) = 67

x² + 32- 16x + 2x² = 67

3x² - 16x + 32 = 67 ( subtract 67 from both sides )

3x² - 16x - 35 = 0 ← in standard form

(x - 7)(3x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = -

Substitute these values into (1) for corresponding values of y

x = 7 : y = 4 - 7 = - 3 ⇒ (7, - 3 )

x = - : y = 4 + = ⇒ (- , )

solutions are (7, - 3 ) and (- , )

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step-by-step explanation: