Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$.
$$\left\{ \begin{array} { c }
x + y = 23 \
x - 2 y = - 13
\end{array} \right.$$
A) $\quad 10$
B) 13
C) $\quad 7$
D) $\quad 8$
E) $\quad 9$

Question

Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$.
$$\left\{ \begin{array} { c } 
x + y = 23 \
x - 2 y = - 13
\end{array} \right.$$
A) $\quad 10$
B) 13
C) $\quad 7$
D) $\quad 8$
E) $\quad 9$

Quizplus · Accepted Answer

To solve the system using Gaussian elimination, we can follow these steps:1. The system of equations is:$$x + y = 23$$$$x - 2y = -13$$2. Subtract the second equation from the first to eliminate $x$:$$(x + y) - (x - 2y) = 23 - (-13)$$$$3y = 36$$$$y = 12$$3. Substitute $y = 12$ into the first equation to find $x$:$$x + 12 = 23$$$$x = 11$$4. Calculate $2x - y$:$$2(11) - 12 = 22 - 12 = 10$$Therefore, the value of $2x - y$ is 10.

Solve the System Using Gaussian Elimination (x,y)( x , y )(x,y)

Solve the System Using Gaussian Elimination $( x , y )$