# Solve the pair of equations using the method of substitution: 3x - y = 8, 5x + y = 0 [2 MARKS].

## Question

Solve the pair of equations using the method of substitution: $3x - y = 8$, $5x + y = 0$ [2 MARKS].

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## Answer

# Solution

**Concept**:
Given the system of equations:

$$ 3x - y = 8 \quad \text{(i)} $$ $$ 5x + y = 0 \quad \text{(ii)} $$

Using the **method of substitution** to solve for $x$ and $y$.

**Step 1**: Solve Equation (ii) for $y$:
$$
5x + y = 0 \
\Rightarrow y = -5x \quad \text{(iii)}
$$

**Step 2**: Substitute the expression for $y$ from (iii) into Equation (i):
$$
3x - (-5x) = 8 \
3x + 5x = 8 \
8x = 8 \
\Rightarrow x = 1
$$

**Step 3**: Substitute $x = 1$ back into Equation (iii) to find $y$:
$$
y = -5(1) = -5
$$

**Conclusion**: The solution to the system of equations is
$$
\mathbf{x = 1} \quad \text{and} \quad \mathbf{y = -5}
$$

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