Solve a pair of linear equations
The idea
A system asks for values of x and y that make both equations true.
Step by step
- A system asks for values of x and y that make both equations true.
- When one equation has +y and the other −y, add them to eliminate y and solve for x.
- Find y by substitution, then check the pair in both original equations.
Example
Which ordered pair (x, y) solves both equations: x + y = 5 and x − y = -1?
Answer
(2, 3)
Add the equations to eliminate y: 2x = 4, so x = 2. Substitute into x + y = 5 to get y = 3. The pair (2, 3) satisfies both equations.
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Solve x + y = 8 and x − y = 2. Check the same point in both equations and describe what it means on a graph.
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