Find solution to the system of linear equations. x1 + 2x2 = 0, 2x1 + 5x2 = 1

x₁ = - 2, x₂ = 1

Step-by-step explanation:

We have the following system of linear equations.

x₁ + 2x₂ = 0

2x₁ + 5x₂ = 1

We will multiply the first equation by 2 and then subtract it from the second equation.

2x₁ + 4x₂ = 0

2x₁ + 5x₂ - (2x₁ + 4x₂) = 1 - 0

2x₁ + 5x₂ - 2x₁ - 4x₂) = 1

x₂ = 1

We can replace this value in the first equation.

x₁ + 2x₂ = 0

x₁ + 2 * 1 = 0

x₁ = - 2