Question

Solve the following system of equations using the elimination method.

0.1x+0.3y=0.9
, 0.1x−0.3y=0.2


(1 point)
Responses

(112,76)
left parenthesis Start Fraction 11 over 2 End Fraction comma Start Fraction 7 over 6 End Fraction right parenthesis

(112,−76)
left parenthesis Start Fraction 11 over 2 End Fraction comma negative Start Fraction 7 over 6 End Fraction right parenthesis

(−76,112)
left parenthesis negative Start Fraction 7 over 6 End Fraction comma Start Fraction 11 over 2 End Fraction right parenthesis

There is no solution

Answer 1

To solve the given system of equations using the elimination method, we start with the following equations:

1. \( 0.1x + 0.3y = 0.9 \) (Equation 1)
2. \( 0.1x - 0.3y = 0.2 \) (Equation 2)

To eliminate \( y \), we can add the two equations together:

\[
(0.1x + 0.3y) + (0.1x - 0.3y) = 0.9 + 0.2
\]

This simplifies to:

\[
0.2x = 1.1
\]

Next, we solve for \( x \):

\[
x = \frac{1.1}{0.2} = 5.5
\]

Now, substituting \( x = 5.5 \) back into one of the original equations to solve for \( y \). We can use Equation 1:

\[
0.1(5.5) + 0.3y = 0.9
\]

Calculate \( 0.1(5.5) \):

\[
0.55 + 0.3y = 0.9
\]

Subtract \( 0.55 \) from both sides:

\[
0.3y = 0.9 - 0.55
\]
\[
0.3y = 0.35
\]

Now, solve for \( y \):

\[
y = \frac{0.35}{0.3} = \frac{35}{30} = \frac{7}{6}
\]

Thus, the solution to the system of equations is:

\[
(x, y) = \left(5.5, \frac{7}{6}\right) = \left(\frac{11}{2}, \frac{7}{6}\right)
\]

Considering the response options, the correct one matches:

\[
\left( \frac{11}{2}, \frac{7}{6} \right)
\]