Question

2х+у=-3 х-2у=-1решите систему

Answer 1

Solving the System of Equations

To solve the system of equations 2x + y = -3 and x - 2y = -1, we can use various methods such as substitution, elimination, or matrix methods. Let's solve it using the substitution method.

1. Solve the first equation for x: 2x + y = -3 Subtract y from both sides: 2x = -3 - y Divide both sides by 2: x = (-3 - y) / 2.

2. Substitute the value of x in the second equation: x - 2y = -1 Replace x with (-3 - y) / 2: ((-3 - y) / 2) - 2y = -1 Simplify the equation: -3 - y - 4y = -2 Combine like terms: -3 - 5y = -2 Add 3 to both sides: -5y = 1 Divide both sides by -5: y = -1/5.

3. Substitute the value of y back into the first equation to find x: 2x + y = -3 Replace y with -1/5: 2x + (-1/5) = -3 Multiply both sides by 5 to eliminate the fraction: 10x - 1 = -15 Add 1 to both sides: 10x = -14 Divide both sides by 10: x = -14/10 = -7/5.

Therefore, the solution to the system of equations 2x + y = -3 and x - 2y = -1 is x = -7/5 and y = -1/5.

Please let me know if you need any further assistance!