Simultaneous Equations
Simultaneous equations involve two or more equations with the same variables. The solution is the set of values that satisfy all equations at the same time.
Common methods of solving include substitution (replacing one variable using another equation) and elimination (adding or subtracting equations to eliminate a variable).
Example
Solve:
\(x + y = 10\)
\(x - y = 2\)
→ add equations: \(2x = 12\)
→ \(x = 6\)
→ substitute: \(6 + y = 10\)
→ \(y = 4\)
Practice
Lvl 2
Solve these simultaneous equations:\[\begin{aligned}x + y &= 7 \\ x - y &= 1\end{aligned}\]
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