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Solve the following simultaneous equations: 2x + y = 7 and x − y = 1.

April 13, 2026Mathematics

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Answer

x = \frac{8}{3}, y = \frac{5}{3}

4 steps

Write down the given simultaneous equations.
$2x + y = 7 \quad (1)$ $x - y = 1 \quad (2)$
Add equation (1) and equation (2) to eliminate $y$ .
$(2x + y) + (x - y) = 7 + 1$ $2x + x + y - y = 8$ $3x = 8$
Solve for $x$ .
$x = \frac{8}{3}$
Substitute the value of $x$ into equation (2) to find $y$ .
$\frac{8}{3} - y = 1$ $-y = 1 - \frac{8}{3}$ $-y = \frac{3}{3} - \frac{8}{3}$ $-y = -\frac{5}{3}$ $y = \frac{5}{3}$
The solution is:
$x = \frac{8}{3}, \quad y = \frac{5}{3}$

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