1.(3x-y) Quadratic -2x Quadratic (4x-5y)-(x+2y), where x = 2009 and y =-2.
Solution: Original formula =(9x? -6xy+y？ )-(8x？ - 10xy)-(x？ +4xy+4y？ )
=9x？ -6xy+y？ -8x？ + 10xy-x？ 4xy-4y？
=-3y？
When x = 2009 and y =-2.
-3y？ =-3*(-2)? =- 12
2. Simplify first, then evaluate
-2x-{4x-2y-[3x-(2y+ 1)}, where x=-3/2 and y=2008.
3. It is known that the m power of 2'x'y and the n power of -3x'y are similar terms, and the value of m-(m power n+3m-4n)+(m'-3n power 2n) is calculated.
4. Given that the quadratic power of' A '-2ab =3 and the quadratic power of' B '-ab =4, then the quadratic power of 2' B '-' A' = ()
2. Simplify first, then evaluate
-2x-{4x-2y-[3x-(2y+ 1)]}, where x=-3/2 and y=2008.
=-2x-{4x-2y-[3x-2y- 1]}
=-2x-{4x-2y-3x+2y+ 1}
=-2x-{4x-3x-2y+2y+ 1}
=-2x-{x+ 1}
=-2x-x- 1
=-3x- 1
=-3*(-3/2)- 1
=9/2- 1
=7/2
3. It is known that the m power of 2'x'y and the n power of -3x'y are similar terms, and the value of m-(m power n+3m-4n)+(m'-3n power 2n) is calculated.
The m power of x and the -3x power of y are similar terms.
That is, the m power of x = x, the 2 power of y = the n power of y.
m= 1
n=2
M-(quadratic power of' m' n+3m-4n)+(quadratic power of 2n' m'-3n)
Quadratic power of = m-' m-' m' n-3m+4n+2n' m '-3n
= m-3m+2n' m quadratic' -'m quadratic' n+4n-3n
=-2m+n' m squared' +n
The second power of =-2* 1+2* 1
=-2+2+2
=2
4. Given that the quadratic power of' A '-2ab =3 and the quadratic power of' B '-ab =4, then the quadratic power of 2' B '-' A' = ()
The quadratic power of 2' b'-'the quadratic power of a'
= 2 ('b'-quadratic power of AB)-('quadratic power of A' -=2('b)
=2*4-3
=8-3
=5
5 .[(x+2)/(x^2-2x)-(x- 1)/(x^2-4x+4)]÷(x^2- 16)/(x^2+4x)
Where X=2+ (arithmetic square root 2)
Solution formula = [(x-4)/x (x-2) 2] [x/(x-4)]
= 1/(x-2)^2= 1/2
factoring
2x？ -Really? -xy-x-2y- 1
=(x+y)(x-y)-x(x-y)-(x-y)-(y- 1)
=(x-y)(y- 1)-(y- 1)
=(x-y- 1)(y- 1)
a^2-b^2+4a+2b+3
=a^2-b^2+4a+2b+4- 1
=(a+2)^2-(b- 1)^2
x？ +y？ -2xy- 10x+ 10y+ 16；
=(x-y)？ - 10(x-y)+ 16
=(x-y-2)(x-y-8)
(x+y)？ -2(x？ -Really? )+(y-x)？
=(x+y)？ -2(x+y)(x-y)+(x-y)？
=[(x+y)-(x-y)]？
=(2y)？
=4y？
(x+ 1)(x+2)+ 1/4
=x^2+2x+x+2+ 1/4
=x^2+3x+9/4
=(x+3/2)^2
Solve five questions in each equation group.
x-y=3，① 3x-8y= 14 ②
Solution: From ①, get
y=x-3 ③
Substitute ③ into ② to get.
3x-8(x-3)= 14
3x-8x+24= 14
-5x+24= 14
-5x= 14-24
-5x=- 10
x=2
Substitute x=2 into ③, and you get
y=2-3=- 1
So the solution of this equation group is
x=2 y=- 1
3m+2n=5m+2，2(3m+2n)= 1 1m+7
Solution: From ①, get
m=n- 1 ③
Substitute ③ into ② to get.
2[3(n- 1)+2n]= 1 1(n- 1)+7
2(3n-3+2n)= 1 1n- 1 1+7
2(5n-3)= 1 1n-4
10n-6= 1 1n-4
10n- 1 1n=-4+6
-n=2
n=-2
Substitute n=-2 into ③ to get.
m=-2- 1=-3
So the solution of this equation group is
m=-3 n=-2
x-3y=2，① x:y=4:3 ②
Solution: From ①, get
x=3y+2 ③
Substitute ③ into ② to get.
(3y+2):y=4:3
3y+2=4y/3
3y-4y/3=-2
5y/3=-2
y=-6/5
Substitute y=-6/5 into ③ to get.
x=3(-6/5)+2=-8/5
So the solution of this equation group is
x=-8/5 y=-6/5
m/2+n/3= 13，① m/3-n/4=3 ②
From (1), we get
m=26-2n/3 ③
Substitute ③ into ① to get.
(26-2n/3)/3-n/4=3
26/3-2n/9-n/4=3
26/3- 17n/36=3
- 17n/36=3-26/3
- 17n/36=- 17/3
n= 12
Substitute n= 12 into ③ to get.
m = 26-2x 12/3 = 26-8 = 18
So the solution of this equation group is
m= 18 n= 12
elimination by substitution
Example: Solve the system of equations x+y = 5 16x+ 13y = 89②.
Solution: Use x=5-y③ to bring ③ from ① to ②, and get 6(5-y)+ 13y=89.
The answer is y=59/7.
Bring y=59/7 into ③ to get x=5-59/7, that is, x=-24/7.
∴x=-24/7,y=59/7
Addition, subtraction and elimination method
Example: Solve the system of equations x+y=9① x-y=5②.
Solution: ①+②, 2x= 14, that is, x=7.
Bring x=7 into ① to get 7+y=9 and y=2.
∴x=7,y=2