Question

Use linear combinations to solve the system of linear equations. $$\begin{aligned} &x+3 y=3\\\ &x+6 y=3 \end{aligned}$$

Short answer

The solution to the system of equations is x = 3, y = 0

Step-by-step solution

Prepare the equations

We start with the system of equations: \[\begin{aligned} x & + 3 y = 3\x & + 6 y = 3 \end{aligned}\]and prepare for computation.

Subtract the Equations

To facilitate solving, we subtract the first equation from the second. In this case, the x variables cancel out, and what we remain with is: \[ 6y - 3y = 3 - 3 \]which simplifies to.\[ 3y = 0 \]

Solve for y

To isolate the variable y, divide the equation by 3:\[ y = 0 \]So, the value for y that satisfies both equations is 0.

Solve for x

Replace y in the first equation with 0 and solve for x:From first equation:\[x + 3*0 = 3 \]Which simplifies to\[ x = 3 \]So, the value for x that satisfies both equations is 3.