Q 231 - Intermediate Algebra

Question

Solve the system of equations by substitution. 

$$\begin{gathered} 3x+y=12 \\ x=y-8 \end{gathered}$$ 

Step-by-Step Solution

Answer

The  solution of the linear equation is that (1,9).

Step 1. Given information

The given linear equations are:$$\begin{gathered} 3x+y=12 \\ x=y-8 \end{gathered}$$

Step 2. Calculation

$$\begin{gathered} \mathrm{First} \mathrm{solve} \mathrm{one} \mathrm{equation} \mathrm{for} \mathrm{one} \mathrm{variable}. \\ \mathrm{Substitute} x = y - 8 \mathrm{in} \mathrm{equation} 3x + y = 12 \mathrm{and} \mathrm{solve} for y. \\ 3x + y = 12 \\ 3(y - 8) + y = 12 \\ 3y - 24 + y = 12 \\ 4y = 12 + 24 \\ 4y = 36 \\ y = 36/4 \\ = 9 \end{gathered}$$

$$\begin{gathered} \mathrm{Substitute} y = 9 \mathrm{into} \\ x = y - 8 \mathrm{and} \mathrm{solve} \mathrm{for} x. \\ x = y - 8 \\ x = 9 - 8 \\ = 1 \end{gathered}$$

$$\begin{gathered} \mathbf{Check}\mathbf{: } \\ \mathrm{First} \mathrm{substitute} x=1 , y = 9 \\ \mathrm{into} \mathrm{the} \mathrm{equation} 3x + y = 12 \\ 3x + y = 12 \\ 3\left(1\right)+9=12 \\ 3+9=12 \\ 12=12 \\ \mathrm{This} \mathrm{is} \mathrm{true}. \\ \mathrm{Also} \mathrm{substitute} x = 1 , y = 9 \mathrm{into} \mathrm{the} \mathrm{equation} \\ x = y - 8 \\ x = y - 8 \\ 1=9-8 \\ 1 = 1 \\ \mathrm{This} \mathrm{is} \mathrm{true}. \mathrm{Therefore}, \mathrm{the} \mathrm{solution} \mathrm{of} \mathrm{the} \mathrm{system} \mathrm{of} \mathrm{linear} \mathrm{equations} \mathrm{is} \mathrm{that} (1,9) \end{gathered}$$