Solve the system by the method of elimination. Round numbers to three decimal places.
$$\left\{ \begin{array} { c }
5.2 x + 8.1 y = 6.9 \
- 2.6 x + 1.1 y = - 0.7
\end{array} \right.$$
A) $( 2.020,1.873 )$
B) $( 0.495,0.534 )$
C) $( - 0.864,1.407 )$
D) $( 0.192,0.728 )$
E) no solution

Question

Solve the system by the method of elimination. Round numbers to three decimal places.
$$\left\{ \begin{array} { c } 
5.2 x + 8.1 y = 6.9 \
- 2.6 x + 1.1 y = - 0.7
\end{array} \right.$$
A) $( 2.020,1.873 )$
B) $( 0.495,0.534 )$
C) $( - 0.864,1.407 )$
D) $( 0.192,0.728 )$
E) no solution

Quizplus · Accepted Answer

To solve the system 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. Multiplying the second equation by 2 to match the x-coefficients:$$5.2x + 8.1y = 6.9$$$$-5.2x + 2.2y = -1.4$$Adding these equations together eliminates $x$:$$10.3y = 5.5$$Solving for $y$:$$y = \frac{5.5}{10.3} \approx 0.534$$To find $x$, substitute $y$ back into one of the original equations. Using the first equation:$$5.2x + 8.1(0.534) = 6.9$$$$5.2x + 4.3254 = 6.9$$$$5.2x = 2.5746$$$$x = \frac{2.5746}{5.2} \approx 0.495$$Thus, the solution is approximately $(0.495, 0.534)$.

Solve the System by the Method of Elimination {5.2x+8.1y=6.9−2.6x+1.1y=−0.7\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.{5.2x+8.1y=6.9−2.6x+1.1y=−0.7​

Solve the System by the Method of Elimination $\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.$