Systems of Equations Math Example 5

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Example 5

hard
Solve: 2x+3y=122x + 3y = 12 and 4x−y=54x - y = 5.

Solution

  1. 1
    From the second equation: y=4x−5y = 4x - 5.
  2. 2
    Substitute into the first: 2x+3(4x−5)=122x + 3(4x - 5) = 12, so 14x−15=1214x - 15 = 12, giving x=2714x = \frac{27}{14}.
  3. 3
    Then y=4(2714)−5=10814−7014=3814=197y = 4\left(\frac{27}{14}\right) - 5 = \frac{108}{14} - \frac{70}{14} = \frac{38}{14} = \frac{19}{7}.

Answer

x=2714,y=197x = \frac{27}{14}, \quad y = \frac{19}{7}
Substitution works even when solutions are fractions. Isolate one variable first, substitute, and simplify carefully.

About Systems of Equations

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

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

Example 2 medium

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Example 3 hard

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Example 4 easy

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