1)solve the simultaneous eqn
3x-y=1
2x^2+2y^2-x+y=11
2)solve equation
a)3^2x-6^x-1=0
3x-y=1
2x^2+2y^2-x+y=11
2)solve equation
a)3^2x-6^x-1=0
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given 3x-y = 1 -----------(i) & 2x^2 +2y^2 -x+ y =1 1------------------------(ii)
from (i) y = 3x- 1 put in (ii)
we get 2x^2 + 2(3x-1)^2 - x + 3x -1 = 11
or 2x^2 + 18x^2 - 12x +2 -x +3x -1 =11
or 20x^2 -10 x - 10 =0
or 2x^2 - x -1 =0
or 2x^2 -2x + x -1 =0
or 2x( x- 1) + 1( x-1 )=0
or ( 2x+1 ) ( x-1) =0 so x= - 1/2 & 1
so y = - 5/2 & 2 so x= - 1/2& 1 & y = - 5/2 & 2 answer
2nd 3^2x- 6^x -1 =0 if it is as
3^2x = 6^x-1 or 2x log3 = x-1 log6
or 2x/x-1 = log6/log3 = 1.63
2x = 1.63 x - 1.63
or x= - 1.63/ .37 = 4.4 answer
from (i) y = 3x- 1 put in (ii)
we get 2x^2 + 2(3x-1)^2 - x + 3x -1 = 11
or 2x^2 + 18x^2 - 12x +2 -x +3x -1 =11
or 20x^2 -10 x - 10 =0
or 2x^2 - x -1 =0
or 2x^2 -2x + x -1 =0
or 2x( x- 1) + 1( x-1 )=0
or ( 2x+1 ) ( x-1) =0 so x= - 1/2 & 1
so y = - 5/2 & 2 so x= - 1/2& 1 & y = - 5/2 & 2 answer
2nd 3^2x- 6^x -1 =0 if it is as
3^2x = 6^x-1 or 2x log3 = x-1 log6
or 2x/x-1 = log6/log3 = 1.63
2x = 1.63 x - 1.63
or x= - 1.63/ .37 = 4.4 answer
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1)3x - y = 1
y = 3x - 1
Substitute in other equation:
2x² + 2(3x-1)² - x + (3x-1) = 11
2x² + 2(9x² - 3x - 3x + 1) - x + 3x - 1 = 11
2x² + 2(9x² - 6x + 1) + 2x - 12 = 0
2x² + 18x² - 12x + 2 + 2x - 12 = 0
20x² - 10x - 10 = 0
2x² - x - 1 = 0
(2x + 1)(x - 1) = 0
x = -½ or 1
Get values of y by substituting in 1st equation:
y=3x-1
When x = -½,
y = 3(-½) -1
y = -5/2
When x = 1,
y = 3(1) - 1
y = 2
2) I haven't figured it out yet
y = 3x - 1
Substitute in other equation:
2x² + 2(3x-1)² - x + (3x-1) = 11
2x² + 2(9x² - 3x - 3x + 1) - x + 3x - 1 = 11
2x² + 2(9x² - 6x + 1) + 2x - 12 = 0
2x² + 18x² - 12x + 2 + 2x - 12 = 0
20x² - 10x - 10 = 0
2x² - x - 1 = 0
(2x + 1)(x - 1) = 0
x = -½ or 1
Get values of y by substituting in 1st equation:
y=3x-1
When x = -½,
y = 3(-½) -1
y = -5/2
When x = 1,
y = 3(1) - 1
y = 2
2) I haven't figured it out yet
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1) y=3x-1 2x^2 +2(3x-1)^2-x +3x-1=11 2x^2 +2 (9x^2-6x+1) +2x-1=11 20x^2-10x-10=0
10(2x^2-x-1)=0 2x^2-2x+x-1=0 (x-1)(2x+1)=0 x=1 or x=-1/2 putting this in y you get result
2)
10(2x^2-x-1)=0 2x^2-2x+x-1=0 (x-1)(2x+1)=0 x=1 or x=-1/2 putting this in y you get result
2)