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1 vote
1 vote
Please help me solve this simultaneous eqn

x+2y=7
2x² + 3y = 5xy-6

User Thom Rogers
by
2.7k points

1 Answer

17 votes
17 votes

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.

User Grabbag
by
2.7k points