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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