Chapter 6.2, Problem 13P

$6y+2x=3$

Writing When solving the system of equations $2x+y=8$ using substitution, which variable will you solve for and which equation will you use to substitute into?

To determine

To find: the variable we will solve for and the equation which we will choose to substitute into

Answer to Problem 13P

Express $y$ from equation $2x+y=8$ in terms of $x$ and substitute into equation $6y+2x=3$

Explanation of Solution

Given information: $6y+2x=3,2x+y=8$

Consider the following equations:

  $\begin{array}{l}6y+2x=3(i)\\ 2x+y=8(ii)\end{array}$

Prefer to choose the equation that has a variable with coefficient 1

Here, the equation $(ii)$ contains a variable $y$ with coefficient 1

From equation $(ii)$ ,

  $y=8-2x$

We will choose equation $(i)$ to substitute $y=8-2x$

Now will solve the equations just to show how will the calculation part becomes easy on choosing the equation that has a variable with coefficient 1(although the solution has not been asked in this question)

Put $y=8-2x$ in $(i)$

  $\begin{array}{l}6\left(8-2x\right)+2x=3\\ \Rightarrow 48-12x+2x=3\\ \Rightarrow 48-10x=3\\ \Rightarrow 48-3=10x\\ \Rightarrow 10x=45\\ \Rightarrow x=\frac{45}{10}=\frac{9}{2}\end{array}$

Put $x=\frac{9}{2}$ in $y=8-2x$

  $y=8-2\left(\frac{9}{2}\right)=8-9=-1$