Q. 4.25 - Intermediate Algebra

Question

For each system of linear equations decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. 

$$\begin{gathered} \left\{\begin{array}{l}4x-5y=-32\\ 3x+2y=-1\end{array}\right. \\ \left\{\begin{array}{l}x=2y-1\\ 3x-5y=-7\end{array}\right. \end{gathered}$$

Step-by-Step Solution

Answer

For a,b elimination and substitution method is preferred respectively

Part (a) Step 1. Given information.

Given the system of equation $\left\{\begin{array}{l}4x-5y=-32\\ 3x+2y=-1\end{array}\right.$

Part (a) Step 2: Checking the method.

The equations are, $$\begin{gathered} 4x-5y=-32 \\ 3x+2y=-1 \end{gathered}$$

Here there are two variables to be found and two equations are given in standard form so the elimination method is more preferred. 

Part (b) Step 1: Given information

Given the system of equations $\left\{\begin{array}{l}x=2y-1\\ 3x-5y=-7\end{array}\right.$

Part (b) Step 2: Checking the method

The equations are, $$\begin{gathered} x=2y-1 \\ 3x-5y=-7 \end{gathered}$$

it is solved for $x$, so the substitution method is more preferred