Solve the system by the method of elimination. Round numbers to three decimal places.
$$\left\{ \begin{array} { c }
5.7 x + 7.1 y = 3.2 \
- 0.8 x - 4.8 y = - 1.1
\end{array} \right.$$
A) $( 2.872,5.844 )$
B) $( 0.348,0.171 )$
C) $( 0.229,0.267 )$
D) $( 0.175,0.310 )$
E) no solution

Question

Solve the system by the method of elimination. Round numbers to three decimal places.
$$\left\{ \begin{array} { c } 
5.7 x + 7.1 y = 3.2 \
- 0.8 x - 4.8 y = - 1.1
\end{array} \right.$$
A) $( 2.872,5.844 )$
B) $( 0.348,0.171 )$
C) $( 0.229,0.267 )$
D) $( 0.175,0.310 )$
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 either $x$ or $y$ in both equations the same. Multiplying the first equation by $0.8$ and the second equation by $5.7$ gives us a system where the coefficients of $x$ in both equations are the same:$$0.8(5.7x + 7.1y) = 0.8(3.2)$$$$5.7(-0.8x - 4.8y) = 5.7(-1.1)$$Simplifying these equations:$$4.56x + 5.68y = 2.56$$$$-4.56x - 27.36y = -6.27$$Adding these equations together to eliminate $x$:$$4.56x + 5.68y - 4.56x - 27.36y = 2.56 - 6.27$$$$-21.68y = -3.71$$Solving for $y$:$$y = \frac{-3.71}{-21.68} \approx 0.171$$To find $x$, substitute $y = 0.171$ into one of the original equations, for example, the first one:$$5.7x + 7.1(0.171) = 3.2$$Solving for $x$:$$5.7x + 1.2141 = 3.2$$$$5.7x = 1.9859$$$$x \approx \frac{1.9859}{5.7} \approx 0.348$$Therefore, the solution is approximately $x = 0.348, y = 0.171$, which corresponds to choice B.

Solve the System by the Method of Elimination {5.7x+7.1y=3.2−0.8x−4.8y=−1.1\left\{ \begin{array} { c } 5.7 x + 7.1 y = 3.2 \\- 0.8 x - 4.8 y = - 1.1\end{array} \right.{5.7x+7.1y=3.2−0.8x−4.8y=−1.1​

Solve the System by the Method of Elimination $\left\{ \begin{array} { c } 5.7 x + 7.1 y = 3.2 \\- 0.8 x - 4.8 y = - 1.1\end{array} \right.$