Chapter 6.2, Problem 1P

Solve each system by substitution. Check your solution.

$x=y$

$x+2y=3$

To determine

To solve: the given system by substitution and to verify the solution.

Answer to Problem 1P

The solution is $(x,y)=(1,1)$

Explanation of Solution

Given information:

The given system is as follows

  $\begin{array}{l}x=y\mathrm{..............}(1)\\ x+2y=\mathrm{3.........}(2)\end{array}$

Calculation:

Solve the system of equations.

Substitute equation $(1)$ in equation $(2)$

  $\begin{array}{l}(2)\Rightarrow \\ x+2y=3\\ y+2y=3\\ 3y=3\\ y=1\\ (1)\Rightarrow x=y=1\end{array}$

Verify the solution.

  $\begin{array}{l}(1)\Rightarrow \\ x=y\\ 1=1\text{ true}\\ (2)\Rightarrow \\ x+2y=3\\ 1+2=3\\ 3=3\text{ true}\end{array}$

Hence, the solution is $(x,y)=(1,1)$