Jawapan

2016-09-14T22:25:19+08:00
3x + y = 6
2x² + y² + 3xy = 6

Arrange both the equations in their general forms first.

3x + y - 6 = 0
2x² + y² + 3xy - 6 = 0

Choose the easier equation to start with, and that's 3x + y - 6 = 0
y = 6 - 3x

Substitute y into 2x² + y² + 3xy - 6 = 0
2x² + (6-3x)² + 3x(6-3x) - 6 = 0
2x² + 9x² - 36x + 36 + 18x - 9x² - 6 = 0
2x² - 18x + 30 = 0

To find the value of x, we can apply the formula of quadratic factors.

[-(b) +/- √(b² - 4ac) ] / 2a

[ -(-18) +/- √(-18² - 4(2)(30)) ] / 2(2)
[ 18 +/- 2√(21) ] / 4

Seperate the calculations into two,
(i)
[18 + 2√(21) ] / 4
= 6.791

(ii)
[18 - 2√(21) ] / 4
= 2.209

x = 6.791 or 2.209

∴ When x = 6.791,
y = 6 - 3(6.791)
   = -14.373

∴ When x = 2.209,
y = 6 - 3(2.209)
   = -0.627

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