Chapter 11, Problem 1CT

To determine

To find: The solution of equations $\left\{\begin{array}{c}-2x+6y=-7\\ 4x+3y=9\end{array}\right\}$ .

Answer to Problem 1CT

The solution of the equation is $\left(3,-1\right)$ .

Explanation of Solution

Given information:

The given equation is $\left\{\begin{array}{c}-2x+6y=-7\\ 4x+3y=9\end{array}\right\}$

Calculation:

Calculate the equation,

Multiply both sides of the equation $-2x+y=-7$ by $-3$ so as to make the soefficients of $y$ negative of one another $6x-3y=21$ .

So,

  $\begin{array}{l}\left\{\begin{array}{c}6x-3y=21\\ 4x+3y=9\end{array}\right\}\\ 10x=30\\ x=3\end{array}$

Substitute 3 for $x$ in $-2x+y=-7$ and simplify.

  $\begin{array}{c}-2\left(3\right)+y=-7\\ y=1\end{array}$

Therefore, the solution in ordered pair from, $\left(3,-1\right)$

In order to check the solution, substitute 3 for $x$ and -1 for $y$ in the given system of equations.

Check: $\begin{array}{l}\left\{\begin{array}{c}-2x+6y=-7\\ 4x+3y=9\end{array}\right\}\\ -2\left(3\right)+-1=-7\\ 4\left(3\right)+3\left(-1\right)=9\end{array}$

Therefore, the solution of the equation is $\left(3,-1\right)$ .