Question

Решите систему уравнений методом подстановки 3х+у=4 { 2х+3у=5

Answer 1

Y=4-3x
подставляем во второе уравнение:
2х+3(4-3х)=5 и решаем:
2х+12-9х-5=0 отсюда
7=7х
х=1
у=4-3=1

Answer 2

System of Equations: Method of Substitution

To solve the system of equations using the method of substitution, we have the following equations:

Equation 1: 3x + y = 4 Equation 2: 2x + 3y = 5

We can solve this system by isolating one variable in one equation and substituting it into the other equation.

Let's solve the system step by step:

Step 1: Solve Equation 1 for y: From Equation 1, we have: 3x + y = 4 y = 4 - 3x

Step 2: Substitute the value of y from Equation 1 into Equation 2: Substituting y = 4 - 3x into Equation 2, we get: 2x + 3(4 - 3x) = 5

Simplifying the equation: 2x + 12 - 9x = 5 -7x + 12 = 5 -7x = 5 - 12 -7x = -7 x = -7 / -7 x = 1

Step 3: Substitute the value of x into Equation 1 to find y: Substituting x = 1 into Equation 1, we get: 3(1) + y = 4 3 + y = 4 y = 4 - 3 y = 1

Therefore, the solution to the system of equations is x = 1 and y = 1.

Answer: The solution to the given system of equations is x = 1 and y = 1.