Systems of Equations Math Example 1

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Example 1

easy
Solve the system: x+y=10x + y = 10 and x−y=4x - y = 4.

Solution

  1. 1
    Add the two equations to eliminate yy: (x+y)+(x−y)=10+4(x+y)+(x-y) = 10+4, giving 2x=142x = 14.
  2. 2
    Solve for xx: x=7x = 7.
  3. 3
    Substitute back into x+y=10x + y = 10: 7+y=107 + y = 10, so y=3y = 3.
  4. 4
    Check in second equation: 7−3=47 - 3 = 4 ✓

Answer

x=7,y=3x = 7, \quad y = 3
The elimination method adds or subtracts equations to remove one variable. This works well when coefficients of one variable are equal (or opposites).

About Systems of Equations

Two or more equations sharing the same variables, where the solution must satisfy all equations simultaneously.

Learn more about Systems of Equations →

More Systems of Equations Examples

Example 2 medium

Solve the system: [formula] and [formula].

Example 3 hard

Solve the system: [formula] and [formula].

Example 4 easy

Solve: [formula] and [formula].

Example 5 hard

Solve: [formula] and [formula].

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