Question

What is the solution to this system?
0.5x - 1.4y = 5.8
y= -0.3x - 1/5

Answer 1

To solve the system of equations given by

1. \( 0.5x - 1.4y = 5.8 \)
2. \( y = -0.3x - \frac{1}{5} \)

we can substitute the expression for \( y \) from the second equation into the first equation.

### Step 1: Substitute for \( y \)

Substituting \( y \) in the first equation:

\[
0.5x - 1.4(-0.3x - \frac{1}{5}) = 5.8
\]

### Step 2: Simplify the equation

Distributing \( -1.4 \):

\[
0.5x + 1.4(0.3)x + 1.4(\frac{1}{5}) = 5.8
\]

Calculating \( 1.4 \times 0.3 \):

\[
0.5x + 0.42x + 1.4(\frac{1}{5}) = 5.8
\]

Calculating \( 1.4 \times \frac{1}{5} = \frac{1.4}{5} = 0.28 \):

\[
0.5x + 0.42x + 0.28 = 5.8
\]

### Step 3: Combine like terms

Combine \( 0.5x \) and \( 0.42x \):

\[
(0.5 + 0.42)x + 0.28 = 5.8
\]

This simplifies to:

\[
0.92x + 0.28 = 5.8
\]

### Step 4: Solve for \( x \)

Subtract \( 0.28 \) from both sides:

\[
0.92x = 5.8 - 0.28
\]
\[
0.92x = 5.52
\]

Now, divide by \( 0.92 \):

\[
x = \frac{5.52}{0.92}
\]

Calculating the above division:

\[
x = 6
\]

### Step 5: Solve for \( y \)

Now, substitute \( x = 6 \) back into the second equation to find \( y \):

\[
y = -0.3(6) - \frac{1}{5}
\]
\[
y = -1.8 - 0.2
\]
\[
y = -2.0
\]

### Final Solution

The solution to the system of equations is:

\[
(x, y) = (6, -2.0)
\]