Calculation of Binary Linear Equations 32x+34y=6, 32x-34y=2

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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