Question

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.

$$\begin{gathered} ⓐ\left\{\begin{array}{l}8x-15y=-32\\ 6x+3y=-5\end{array}\right. \\ ⓑ\left\{\begin{array}{l}x=4y-3\\ 4x-2y=-6\end{array}\right. \end{gathered}$$

Short answer

Part (a) Elimination

Part (b) Substitution

Step-by-step solution

Part(a) Step 1. Given Information 

The given equations are as:

$$\begin{gathered} \left\{\begin{array}{l}8x-15y=-32\\ 6x+3y=-5\end{array}\right. \\ \left\{\begin{array}{l}x=4y-3\\ 4x-2y=-6\end{array}\right. \end{gathered}$$

Part(a) Step 2. Convenient method to solve the equations

In a) part equations are

$\left\{\begin{array}{l}8x-15y=-32\\ 6x+3y=-5\end{array}\right.$

The above 2 equations are in the standard form and if we will multiply the 2nd equation by 5 and then just add the two linear equations, it will be very easy to solve.

Therefore Elimination will be best to solve the part a.

Part(b) Step 1. Given Information 

We are given system of linear equation,

$\left\{\begin{array}{l}x=4y-3\\ 4x-2y=-6\end{array}\right.$

It can be easily seen that if we will substitute the value of $x$from the first equation to the second. We will get the value of $y$.

Therefore substitution will be the best method to solve part b.

Part(b) Step 2. Convenient method to solve the equations 

It can be easily seen that if we will substitute the value of $x$from the first equation to the second. We will get the value of $y$.

Therefore substitution will be the best method to solve part $b$.