Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { c }
5 x + 7 y = 21 \
- 14 x - 18 y = - 38
\end{array} \right.$
A) (14, 13)
B)(-14, -13)
C)(-14, 14)
D)(-14, 13)
E)(14, -13)

Question

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically.   $\left\{ \begin{array} { c } 
5 x + 7 y = 21 \
- 14 x - 18 y = - 38
\end{array} \right.$  
A) (14, 13)
B)(-14, -13) 
C)(-14, 14)
D)(-14, 13)
E)(14, -13)

Quizplus · Accepted Answer

To solve the system of equations by elimination, we first aim to eliminate one of the variables by making the coefficients of that variable the same (in absolute value) in both equations. We can do this by multiplying the first equation by 2 and the second equation by 1 (to simplify calculations, we notice that multiplying the first equation by 2 will make the coefficients of $y$ in both equations equal in magnitude):First equation after multiplying by 2:$$2(5x + 7y) = 2(21)$$$$10x + 14y = 42$$Second equation remains the same:$$-14x - 18y = -38$$Now, we add both equations together to eliminate $y$:$$10x + 14y - 14x - 18y = 42 - 38$$$$-4x - 4y = 4$$Dividing the entire equation by -4 gives:$$x + y = -1$$  (Equation 1)To find the value of one of the variables, we can substitute the value of $x$ from Equation 1 into one of the original equations. Let's use the first original equation for simplicity:$$5x + 7y = 21$$Since $x + y = -1$, we can express $x$ as $x = -1 - y$. Substituting this into the first original equation gives:$$5(-1 - y) + 7y = 21$$$$-5 - 5y + 7y = 21$$$$2y = 26$$$$y = 13$$Substituting $y = 13$ into $x + y = -1$ gives:$$x + 13 = -1$$$$x = -14$$Therefore, the solution to the system of equations is $x = -14$ and $y = 13$, which corresponds to choice D.

Solve the System of Linear Equations by the Method of Elimination.Find