Chapter 12.8, Problem 1MRE

To determine

To calculate: The solution set for the system of equations with the help either substitution or elimination.

  $\begin{array}{l}3x-2y=1\\ x-y=0\end{array}$

Answer to Problem 1MRE

The solution set for the system of equations is $\left(1,1\right)$ .

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{l}3x-2y=1\\ x-y=0\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{l}3x-2y=1\\ x-y=0\end{array}$

Use the method of substitution to solve the system above.

From the equation $x-y=0$ isolate the value of y ,

  $\begin{array}{c}x-y=0\\ -y=-x\\ y=x\end{array}$

Now substitute $y=x$ in the equation $3x-2y=1$ ,

  $\begin{array}{c}3x-2\left(x\right)=1\\ 3x-2x=1\\ x=1\end{array}$

Now, substitute $x=1$ in the equation $y=x$ ,

  $\begin{array}{c}y=x\\ y=1\end{array}$

Therefore, solution is the coordinate pair, $\left(1,1\right)$ .

Thus, the solution set for the system of equations is $\left(1,1\right)$ .