Question

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

$$\begin{gathered} \left(a\right)\left\{\begin{array}{l}y=4x+9\\ 5x-2y=-21\end{array}\right. \\ \left(b\right)\left\{\begin{array}{l}9x-4y=24\\ 3x+5y=-14\end{array}\right. \end{gathered}$$

Short answer

Part (a): We can see that one equation is already solved for y so using substitution will be most convenient.

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

Step-by-step solution

Part (a) Step 1. Given information

We have been given equation:$\left\{\begin{array}{l}y=4x+9\\ 5x-2y=-21\end{array}\right.$

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

For the given equation:$\left\{\begin{array}{l}y=4x+9\\ 5x-2y=-21\end{array}\right.$

Since one equation is already solved for $y$, So using substitution will be the most convenient method.

By substituting $y$of first equation in the second equation we can easily solve for $x$

Part (b) Step 1. Given information

We have been given equation:$\left\{\begin{array}{l}9x-4y=24\\ 3x+5y=-14\end{array}\right.$

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

For the given equation:$\left\{\begin{array}{l}9x-4y=24\\ 3x+5y=-14\end{array}\right.$

We can see that both equations are in standard form, so using elimination will be the most convenient method.