Solve system: x+y=10 and x-y=4

Problem

$\begin{cases} x + y = 10 \\ x - y = 4 \end{cases}$

Step-by-step solution

Add the two equations to eliminate $y$ : $(x+y) + (x-y) = 10 + 4$ , giving $2x = 14$ .
Solve: $x = 7$ .
Substitute back into the first: $7 + y = 10$ , so $y = 3$ .
Verify: $7 - 3 = 4$ ✓.

Answer

$(x, y) = (7, 3)$

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