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 in front of either $x$ or $y$ the same in both equations. Multiplying the second equation by 2 to match the coefficient of $x$ in the first equation gives us:Original system:$$5.2x + 8.1y = 6.9$$$$-2.6x + 1.1y = -0.7$$Modified system:$$5.2x + 8.1y = 6.9$$$$-5.2x + 2.2y = -1.4$$Adding these equations together to eliminate $x$:$$0x + 10.3y = 5.5$$Solving for $y$:$$y = \frac{5.5}{10.3} \approx 0.534$$Substituting $y = 0.534$ into one of the original equations to solve for $x$, using the second equation for simplicity:$$-2.6x + 1.1(0.534) = -0.7$$$$-2.6x + 0.5874 = -0.7$$$$-2.6x = -1.2874$$$$x = \frac{-1.2874}{-2.6} \approx 0.495$$Therefore, the solution to the system is approximately $(0.495, 0.534)$, which matches choice B.

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 $\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.$