Question

Choose a method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{aligned} &3 x+6 y=8\\\ &-6 x+3 y=2 \end{aligned} $$

Short answer

The solution to the system of equations is \(x = 2/3\) and \(y = 10/9\).

Step-by-step solution

Arrange the equations for elimination

Align the like terms vertically. The system is already arranged in this form: \(3x + 6y = 8\) and \(-6x + 3y = 2\).

Add the two equations

To eliminate x, add \((3x + 6y = 8)\) and \((-6x + 3y = 2)\) together. This gives us \(9y = 10\).

Solve for y

To find the value of y, divide both sides of the equation by 9. This yields \(y = 10/9\).

Substitute y into one of the original equations

Substitute y = 10/9 into the first equation \(3x + 6y = 8\). This yields the equation \(3x + 60/9 = 8\).

Solve for x

To find the value of x, subtract 60/9 from both sides and divide the result by 3, this gives \(x = 72/90 - 60/90 = 12/90 = 2/3\).