Q. 31 - Precalculus Enhanced with Graphing Utilities

Question

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{c}2x-3y=-1\\ 10x+y=11\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given system of equation is $x=1, y=1; \left(1,1\right)$.

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}2x-3y& =& -1\\ 10x+y& =& 11\end{array}$

Step 2. Determine one variable in terms of another variable.

The second equation can be written as:

$\begin{array}{rcl}10x+y& =& 11\\ y& =& 11-10x\end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the first equation.

$\begin{array}{rcl}2x-3(11-10x)& =& -1\\ 2x-33+30x& =& -1\\ 32x& =& -1+33\\ x& =& \frac{32}{32}\\ x& =& 1\end{array}$

Step 4. Determine the value of another variable.

Substitute $x=1$ in $y=11-10x$.

$\begin{array}{rcl}y& =& 11-10\left(1\right)\\ y& =& 11-10\\ y& =& 1\end{array}$

The solution of the given system of equation is $x=1, y=1; \left(1,1\right)$.