Question

Помогите решить систему 1) {2х+у=5 {Х+2у=0 2) {7х+У=20 {х-5у=8

Answer 1

1)2x+y=5
   x+2y=0
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  2x+y=5
  x=-2y
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 2(-2y)+y=5
 x=-2y
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-4y+y=5, -3y=5, y=-5/3
x=-2(-5/3), x=10/3
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/x,y/=/10/3, -5/3/
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2)7x+y=20
   x-5y=8
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  7x+y=20
  x=8+5y
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  7(8+5y)+y=20, 56+36y=20,36y=20-56,36y=-36, y=-1
   x=8+5(-1),x=8-5, x=3
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/x,y/=/3,-1/
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Answer 2

Solving the System of Equations

To solve the system of equations:

1) 2x + y = 5 x + 2y = 0

2) 7x + y = 20 x - 5y = 8

we can use the method of substitution or elimination. Let's solve it using the method of substitution.

Method of Substitution

Step 1: Solve one equation for one variable in terms of the other variable.

From the first equation, we can solve for x in terms of y: 2x + y = 5 2x = 5 - y x = (5 - y)/2

Step 2: Substitute the expression for the variable found in step 1 into the other equation.

Substituting x = (5 - y)/2 into the second equation: x + 2y = 0 (5 - y)/2 + 2y = 0

Step 3: Solve the resulting equation for the remaining variable.

Let's simplify the equation: (5 - y)/2 + 2y = 0 5 - y + 4y = 0 5 + 3y = 0 3y = -5 y = -5/3

Step 4: Substitute the value of the remaining variable back into one of the original equations to solve for the other variable.

Substituting y = -5/3 into the first equation: 2x + y = 5 2x + (-5/3) = 5 2x - 5/3 = 5 2x = 5 + 5/3 2x = 20/3 x = (20/3)/2 x = 20/6 x = 10/3

Solution

The solution to the system of equations is x = 10/3 and y = -5/3.

Please let me know if there's anything else I can help you with!