Question

To decide whether it would be more convenient to solve the system of equations by substitution or

elimination.

$$\begin{gathered} \left(a\right)\left\{\begin{array}{l}14x-15y=-30\\ 7x+2y=10\end{array}\right. \\ \left(b\right)\left\{\begin{array}{l}x=9y-11\\ 2x-7y=-27\end{array}\right. \end{gathered}$$

Short answer

Part (a): We can see that both the equations are in standard form, so using elimination will be most convenient.

Part (b): We can see that one equation is already solved for $x$, so using substitution will be most convenient.

Step-by-step solution

Part (a) Step 1. Given information

Given equation:$\left\{\begin{array}{l}14x-15y=-30\\ 7x+2y=10\end{array}\right.$

Part (a) Step 2. Deciding the most convenient method

For given equation:$\left\{\begin{array}{l}14x-15y=-30\\ 7x+2y=10\end{array}\right.$

Using elimination method will be most convenient. Since both equations are in standard form and can easily be solved by elimination one variable.

Part (b) Step 1. Given information 

Given equation:$\left\{\begin{array}{l}x=9y-11\\ 2x-7y=-27\end{array}\right.$

Part (b) Step 2. Deciding the most convenient method

For given equation:$\left\{\begin{array}{l}x=9y-11\\ 2x-7y=-27\end{array}\right.$

Using substitution method will be most convenient. Since we can easily substitute value of$x$from first equation in to the second equation and solving for$y$