The solution to the pair of simultaneous equation using substitution method is (x,y) = (-2/3, -25/3) or (3, -1)
How to solve simultaneous equation
2x - y = 7 (1)
x² + xy = 6 (2)
From (1)
-y = 7 - 2x
y = 2x - 7 (3)
- substitute y = 2x - 7 into (2)
x² + x(2x - 7) = 6
x² + 2x² - 7x = 6
3x² - 7x - 6 = 0
- solve the quadratic equation using formula
x = (-b ±√b² - 4ac) / 2a
= -(-7) ± √(-7)² - 4(3)(-6) / 2(3)
= 7 ± √49 - (-72) / 6
= 7 ± √121 / 6
= (7 ± 11) / 6
x = 18/6 or -4/6
x = 3 or -2/3
when x = 3
y = 2x - 7
= 2(3) - 7
= 6 - 7
y = -1
when x = -2/3
y = 2x - 7
= 2(-2/3) - 7
= -4/3 - 7
= (-4-21) / 3
= -25/3
So,
(x,y) = (-2/3, -25/3) or (3, -1)
The variation formula to represent the statement is
y = k / √x
where,
k = constant of proportionality
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