Question

Solve this pair of simultaneous equations algebraically
x²-y²+xy=20
x =2y​

Answer 1

There are two sets of solutions

(4, 2) and (-4, -2)

Explanation:

x² - y² + x · y=20 (1)

x = 2y (2)

Substitute x = 2y in equation (1)

==> (2y)² - y² + (2y)y = 20

==> 4y² - y² + 2y² = 20

==> 5y² = 20

==> y² = 20/5

==> y² = 4

==> y = ± √4

==> y = ±2

For y = +2,

x = 2(2) in equation (2)

==> x = 4

For y = -2

x = 2(-2) = -4 in equation (2)

Hence the solution pairs are
(4, 2) and (-2, -4)