Question

Find solution to the system of linear equations. 3x1 + 6x2 = 2 , 9x1 + 12x2 = 1

Answer 1

x₁ = -1

x₂ = 5/6

Explanation:

The equations of the given linear system are:

`3x_1 +6x_2=2\\9x_1 +12x_2 = 1`

Multiply the first equation by -2 and add it to the second one to solve for x₁:

`-6x_1 -12x_2=-4\\9x_1 +12x_2 +(-6x_1 -12x_2)= 1-4\\3x_1=-3\\x_1=-1`

Since we already know the value of x₁, simply replace it in the first equation to solve for x₂:

`3x_1 +6x_2=2\\x_2=(2+3)/(6) =(5)/(6)`

The solution for the system is x₁ = -1 and x₂ = 5/6