Answer:
x = 11/9 and y = 26/9 or x = 3 and y = 2
Explanation:
x + 2y = 7 --1
2x² + 3y = 5xy - 6 --2
From 1, make x the subject.
x = 7 - 2y
Substitute x = 7 - 2y into 2.
2(7 - 2y)² + 3y = 5y(7 - 2y) - 6
Simplify and solve for y.
2(49 - 28y + 4y²) + 3y = 35y - 10y² - 6
98 - 56y + 8y² + 3y = 35y - 10y² - 6
18y² - 88y + 104 = 0
9y² - 44y + 52 = 0
Factorise.
(9y - 26)(y - 2) = 0
9y - 26 = 0 or y - 2 = 0
9y = 26 or y = 2
y = 26/9 or y = 2
Substitute values of y into x = 7 - 2y.
x = 7 - 2(26/9) or x = 7 - 2(2)
= 11/9 = 3
Thus, x = 11/9 and y = 26/9 or x = 3 and y = 2.