Question

3x²+5xy=–4
xy–2x=—3

`solve simultinously`
​

Answer 1

`xy - 2x = - 3`

`xy = 2x - 3`

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`3 {x}^(2) + 5xy + 4 = 0`

`3 {x}^(2) + 5(2x - 3) + 4 = 0`

`3 {x}^(2) + 10x - 15 + 4 = 0`

`3 {x}^(2) + 10x - 11 = 0`

`delta = {10}^(2) - 4(3)( - 11)`

`delta = 100 + 132`

`delta = 232`

Thus;

`x = ( - 10 + √(232) )/(6) \: \: or \: \: x ( - 10 - √(232) )/(6) \\`

`x = ( - 10 + 15.23)/(6) \: \: or \: \: x = ( - 10 - 15.23)/(6) \\`

`x = (5.23)/(6) \: \: or \: \: x = ( - 25.23)/(6) \\`

`x = 0.8716 \: \: or \: \: x = - 4.205`

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If x = 0.8716 then :

`0.8716 \: y = 2(0.8716) - 3`

`0.8716 \: y = 1.7432 - 3`

`0.8716 y= - 1.2568`

`y = ( - 1.2568)/(0.8716) \\`

`y = - 1.4419`

And if x = - 4.205 then :

`- 4.205 \: y = 2( - 4.205) - 3`

`- 4.205 \: y = - 8.410 - 3`

`- 4.205 \: y = - 11.410`

`y = ( - 11.410)/( - 4.205) \\`

`y = 2.7134`

And we're done

Have a great day ♡