Question

Номер 1512 решите систему уравнений способом подстановки 15+2(х+3у)=3(4х+у) 2(5х-2у)-3у=2+3(2х-у)

Answer 1

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Answer 2

To solve the system of equations using the method of substitution, we need to follow these steps:

Step 1: Solve one of the equations for one of the variables. Step 2: Substitute the expression obtained from Step 1 into the other equation. Step 3: Solve the resulting equation for the remaining variable. Step 4: Substitute the value of the variable found in Step 3 back into the expression obtained in Step 1 to find the value of the other variable.

Let's go through these steps:

Given system of equations:

1. 15 + 2(x + 3y) = 3(4x + y)
2. 2(5x - 2y) - 3y = 2 + 3(2x - y)

Step 1: Let's solve equation (1) for x: 15 + 2(x + 3y) = 3(4x + y)

First, simplify the equation: 15 + 2x + 6y = 12x + 3y

Now, move all x terms to one side and all y terms to the other side: 2x - 12x = 3y - 6y -10x = -3y

Divide both sides by -10: x = 3y/10

Step 2: Now that we have an expression for x in terms of y, we will substitute this expression into equation (2):

2(5x - 2y) - 3y = 2 + 3(2x - y)

Substitute x with 3y/10: 2(5(3y/10) - 2y) - 3y = 2 + 3(2(3y/10) - y)

Step 3: Now, solve for y:

2(3y/2 - 2y) - 3y = 2 + 3(3y/5 - y)

Simplify the equation: 3y - 4y - 3y = 2 + 3(3y/5 - y)

Combine like terms: -4y = 2 + 3(3y/5 - y)

Step 4: Now, solve for y:

-4y = 2 + 3(3y/5 - 5y/5)

Simplify further: -4y = 2 + 3(3y - 5y)/5 -4y = 2 + 3(-2y)/5

Multiply through by 5 to eliminate the fraction: -20y = 10 - 6y

Add 6y to both sides: -20y + 6y = 10

Combine like terms: -14y = 10

Finally, divide both sides by -14 to solve for y: y = -10/14 y = -5/7

Step 5: Now that we have the value of y, we can find the value of x using the expression we derived earlier:

x = 3y/10 x = 3*(-5/7)/10 x = -15/70 x = -3/14

So, the solution to the system of equations is: x = -3/14 y = -5/7