Question

Solve algebraically x2 + y2 = 18 x-2y=-3

Answer 1

Answer:

(- $\frac{3}{5}$, - $\frac{21}{5}$ ) and (3, 3 )

Step-by-step explanation:

Given the 2 equations

x² + y² = 18 → (1)

x - 2y = - 3 → (2)

Rearrange (2) expressing x in terms of y by adding 2y to both sides.

x = 2y - 3 → (3)

Substitute x = 2y - 3 into (1)

(2y - 3)² + y² = 18 ← expand left side and simplify

4y² - 12y + 9 + y² = 18

5y² - 12y + 9 = 18 ( subtract 18 from both sides )

5y² - 12y - 9 = 0 ← in standard form

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

Equate each factor to zero and solve for y

5y + 3 = 0 ⇒ 5y = - 3 ⇒ y = - $\frac{3}{5}$

y - 3 = 0 ⇒ y = 3

Substitute these values into (3) for corresponding values of x

y = - $\frac{3}{5}$ : x = - $\frac{6}{5}$ - 3 = - $\frac{21}{5}$ ⇒ ( - $\frac{3}{5}$, - $\frac{21}{5}$ )

y = 3 : x = 6 - 3 = 3 ⇒ (3, 3 )