Question

Choose a method to solve the linear system. Explain your choice. $$ \begin{aligned} &x+y=300\\\ &x+3 y=18 \end{aligned} $$

Short answer

The solution to the system of linear equations is x = 441 and y = -141.

Step-by-step solution

Arrange the equations

Arrange the system vertically, aligning like terms:\[\begin{align*}x + y &= 300 \\x + 3y &= 18\end{align*}\]

Applying the Elimination Method

Subtract the second equation from the first (since the coefficients of 'x' are the same). This will eliminate 'x' and you will get an equation in 'y': \[\begin{align*}(x + y) - (x + 3y) &= 300 - 18 \\-2y &= 282\end{align*}\]

Solving for 'y'

Next, divide by -2 to solve for y:\[\begin{align*}y &= \frac{282}{-2} \\y &= -141\end{align*}\]

Solving for 'x'

After finding y, substitute y = -141 into the first equation to solve for x:\[\begin{align*}x + y &= 300 \\x - 141 &= 300 \\x &= 300 + 141 \\x &= 441\end{align*}\]