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

Question

Quizplus · Accepted Answer

To solve the system by elimination, we first aim to eliminate one of the variables by making the coefficients in front of either $x$ or $y$ the same in both equations. Multiplying the second equation by 2 to match the $x$ coefficient in the first equation gives us:Original system:1) $5.2x + 8.1y = 6.9$2) $-2.6x + 1.1y = -0.7$Modified system:1) $5.2x + 8.1y = 6.9$2) $-5.2x + 2.2y = -1.4$Adding the two equations to eliminate $x$:$10.3y = 5.5$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 second equation:$-2.6x + 1.1(0.534) = -0.7$Solving for $x$:$-2.6x = -0.7 - 1.1(0.534)$$-2.6x = -0.7 - 0.5874$$-2.6x = -1.2874$$x = \frac{-1.2874}{-2.6} \approx 0.495$Thus, the solution is approximately $x = 0.495, y = 0.534$, which corresponds to choice B.

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

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