Main contents:
The main feature of the equation in this example is that the unknown coefficients are equal, that is, the main methods and steps to calculate the binary linear equations 32x+34y=6, 32x-34y=2 are introduced.
Main steps:
Equality addition and subtraction ※
1) equation addition:
32x+34y=6……①,
32x-34y=2……②
Then ①+② has:
You can get 64x=6+2 and x= 1/8.
Substituting x into equation ① includes:
32* 1/8+34y=6,
34y=2, that is, y =117,
Then the solution of the equation is: x= 1/8, y =117.
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2) Equation subtraction:
32x+34y=6……①,
32x-34y=2……②
Then ①-② have:
Y= 1/ 17,
Substituting y into equation ① includes:
32*x+34*( 1/ 17)=6,
32x=4, which means x= 1/8.
Then the solution of the equation is: x= 1/8, y =117.
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Substitution method. ※
1) elimination x method
Substitute 34y=6-32x in ① into Formula ②:
32x-(6-32x)= 2,
64x-6=2,
64x=6+2,x= 1/8,
Substituting x into equation ① includes:
32* 1/8+by=6,
34y=2, that is, y =117,
Then the solution of the equation is: x= 1/8, y =117.
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2) Elimination of Y method
32x=6-34y from ①, and substitute it into Equation ②:
6-34y-34y=2,
6-68y=2,
You can get 68y=6-2, y =117.
Substituting y into equation ① includes:
32*x+34*( 1/ 17)=6,
32x=4, which means x= 1/8.
Then the solution of the equation is: x= 1/8, y =117.
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. Determinant method ※
Coefficient determinant d0 of the equation = | 32,34; 32,-34|=- 1088- 1088=-2 176;
Determinant dx = | 6,34 of the equations corresponding to x; 2,-34|=-204-68=-272;
The determinant of the equation corresponding to y, dy = | 32,6,32,2 | = 64-192 =-128;
Then the solution of the system of equations x is:
x = Dx/D0 =-272/-2 176 = 1/8,
y = Dy/D0 =- 128/-2 176 = 1/ 17 .
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