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Use the substitution method to solve these pairs of simultaneous equations.

August 12, 2026Mathematics

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Answer

x = 9

y = 1

5 steps

Here's how to solve question 1 using the substitution method:

Write down the given equations.
$x + y = 10 \quad \cdots (1)$ $x - y = 8 \quad \cdots (2)$
From equation (2), express $x$ in terms of $y$ .
$x = 8 + y \quad \cdots (3)$
Substitute equation (3) into equation (1).
$(8 + y) + y = 10$ $8 + 2y = 10$
Solve for $y$ .
$2y = 10 - 8$ $2y = 2$ $y = \frac{2}{2}$ $y = 1$
Substitute the value of $y$ back into equation (3) to find $x$ .
$x = 8 + 1$ $x = 9$
The solution is:
$x = \boxed{9}$ $y = \boxed{1}$

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