Question

Система уравнений: 2x+y=12 3x-5y=5

Answer 1

System of Equations: 2x + y = 12, 3x - 5y = 5

To solve the system of equations: - 2x + y = 12 - 3x - 5y = 5

We can use various methods such as substitution, elimination, or matrix methods. Let's solve it using the substitution method.

Substitution Method:

Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for y:

From the first equation, we have: 2x + y = 12

Solving for y, we get: y = 12 - 2x

Step 2: Substitute the expression for y in the second equation.

Substituting y = 12 - 2x into the second equation, we get: 3x - 5(12 - 2x) = 5

Simplifying the equation, we have: 3x - 60 + 10x = 5 13x - 60 = 5 13x = 65 x = 5

Step 3: Substitute the value of x back into one of the original equations to solve for y.

Using the first equation: 2x + y = 12 2(5) + y = 12 10 + y = 12 y = 2

Therefore, the solution to the system of equations is x = 5 and y = 2.

Note: The solution to the system of equations is x = 5 and y = 2.