Systems of Equations Math Example 2

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Example 2

medium
Solve the system: y=2x+1y = 2x + 1 and 3x+y=113x + y = 11.

Solution

  1. 1
    Since y=2x+1y = 2x + 1, substitute into the second equation: 3x+(2x+1)=113x + (2x + 1) = 11.
  2. 2
    Simplify: 5x+1=115x + 1 = 11.
  3. 3
    Subtract 1: 5x=105x = 10, so x=2x = 2.
  4. 4
    Find yy: y=2(2)+1=5y = 2(2) + 1 = 5.
  5. 5
    Check: 3(2)+5=113(2) + 5 = 11 ✓

Answer

x=2,y=5x = 2, \quad y = 5
The substitution method replaces one variable with an equivalent expression from the other equation, reducing the system to a single equation in one variable.

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 1 easy

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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