In mathematics, substitution is a process of replacing a variable or expression with another expression that has the same value. Substitution is commonly used to simplify expressions, solve equations, and evaluate functions.
For example, if we have the expression:
3x + 2y – 4
And we know that x = 2 and y = 5, we can substitute those values into the expression to get:
3(2) + 2(5) – 4 = 6 + 10 – 4 = 12
So the expression simplifies to 12.
Another example of substitution is when solving equations. For instance, if we have the equation:
2x + 5 = 13
We can solve for x by using substitution. First, we isolate x by subtracting 5 from both sides:
2x = 8
Then, we divide both sides by 2 to get:
x = 4
This is our solution for x. We can check that it is correct by substituting x = 4 back into the original equation:
2(4) + 5 = 13
And we can see that the left-hand side of the equation simplifies to 13, which is equal to the right-hand side, confirming that x = 4 is a valid solution to the equation.