Question

1. 0.3x + y = 0.1

0.1x + 0.2y = -0.1

Explanation:

Step1: Multiply equations to eliminate decimals

Multiply the first equation \(0.3x + y = 0.1\) by 10: \(3x + 10y = 1\) (Equation 1).
Multiply the second equation \(0.1x + 0.2y = -0.1\) by 10: \(x + 2y = -1\) (Equation 2).

Step2: Solve Equation 2 for x

From \(x + 2y = -1\), we get \(x = -1 - 2y\).

Step3: Substitute x into Equation 1

Substitute \(x = -1 - 2y\) into \(3x + 10y = 1\):
\(3(-1 - 2y) + 10y = 1\)
\(-3 - 6y + 10y = 1\)
\(4y = 4\)
\(y = 1\).

Step4: Find x using y

Substitute \(y = 1\) into \(x = -1 - 2y\):
\(x = -1 - 2(1) = -3\).

Answer:

\(x = -3\), \(y = 1\)