Question

Is (–5, 0.5) a solution of this system?

x – 4y = –7,

0.2x + 2y = 0

Substitute (–5, 0.5) into x – 4y = –7 to get
.
Substitute (–5, 0.5) into 0.2x + 2y = 0 to get
.
Simplify the above equations to get

Answer 1

To determine if \((-5, 0.5)\) is a solution of the given system of equations, we will substitute \(x = -5\) and \(y = 0.5\) into each equation.

### First Equation:
\[ x - 4y = -7 \]

Substituting \((-5, 0.5)\):
\[
-5 - 4(0.5) = -7
\]
Calculating:
\[
-5 - 2 = -7
\]
This simplifies to:
\[
-7 = -7 \quad \text{(True)}
\]

### Second Equation:
\[ 0.2x + 2y = 0 \]

Substituting \((-5, 0.5)\):
\[
0.2(-5) + 2(0.5) = 0
\]
Calculating:
\[
-1 + 1 = 0
\]
This simplifies to:
\[
0 = 0 \quad \text{(True)}
\]

### Conclusion:
Both equations are satisfied, therefore \((-5, 0.5)\) is a solution of the system.