Substitution Math Example 4

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Example 4

medium
If u=2v−1u = 2v - 1 and 3u+v=113u + v = 11, find vv.

Solution

  1. 1
    Substitute u=2v−1u = 2v - 1 into 3u+v=113u + v = 11: 3(2v−1)+v=113(2v - 1) + v = 11.
  2. 2
    Simplify: 6v−3+v=116v - 3 + v = 11, so 7v=147v = 14, giving v=2v = 2.

Answer

v=2v = 2
Substituting an expression for a variable reduces a two-variable problem to a single-variable equation.

About Substitution

Replacing every occurrence of a variable or sub-expression with an equivalent value or expression throughout a problem.

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More Substitution Examples

Example 1 easy

If [formula] and [formula], find [formula].

Example 2 medium

If [formula] and [formula], use substitution to solve for [formula].

Example 3 easy

Evaluate [formula] when [formula] and [formula].

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