Chapter 3.1, Problem 4AGP

To determine

To solve the system of linear equations using substitution method.

Answer to Problem 4AGP

  $x=4,$

  $y=-1$

Explanation of Solution

Given information: A system of linear equations

  $5x-3y=23\mathrm{...}\text{(1)}$

  $2x+y=7\mathrm{...}\text{(2)}$

Calculation: According to substitution method, we need to solve one of the equation for a variable x or y and then substitute it in another equation and solve for another variable.

So, first we solve second equation $2x+y=7$ for y .

Subtracting 2x on both sides, we get

  $2x+y-2x=7-2x$

  $\Rightarrow y=-2x+7$

Now, substitute $y=-2x+7$ in first equation $5x-3y=23$

  $5x-3(-2x+7)=23$

  $\Rightarrow 5x+6x-21=23$

Combine like terms

  $11x-21=23$

Adding 21 on both sides

  $\begin{array}{l}11x-21+21=23+21\\ \Rightarrow 11x=44\end{array}$

Divide both sides by 11

  $\begin{array}{l}\frac{11x}{11}=\frac{44}{11}\\ \Rightarrow x=4\end{array}$

Plug $x=4$ in $y=-2x+7$ , we get

  $\begin{array}{l}y=-2(4)+7=-8+7\\ \Rightarrow y=-1\end{array}$

Therefore, solution of the given system is $x=4,$

  $y=-1$ .