Substitute means to replace a variable with a number or with an equal expression. In 4x − 1, substituting 3 for x gives 4(3) − 1. You substitute to evaluate expressions, to check whether a number is a solution, and to solve systems of equations by swapping in an equal expression.
Substituting means swapping a variable for something equal to it: a number, or a whole expression in parentheses.
Formal definition and notation
Substitution replaces every occurrence of a variable in an expression or equation by a given number or by an expression known to be equal to it. By the substitution property of equality, if a = b, then b may replace a in any expression or equation without changing its value or its truth.
Symbol
Read it as
Meaning
x = 3
x equals 3
the replacement: put 3 wherever x appears
4(3) − 1
4 times 3 minus 1
the expression after substituting, with the number in parentheses
y = 2x
y equals 2 x
an expression for y that can be substituted into another equation
Key facts
Every copy of the variable gets the same value: in x2 + x at x = 2, both copies become 2, giving 4 + 2 = 6.
To check a solution, substitute it into the original equation. If both sides come out equal, it is a solution; if not, it is not.
You can substitute an expression, not just a number: with y = x + 4, the equation 2x + y = 10 becomes 2x + (x + 4) = 10.
Substituting an expression is the heart of the substitution method for systems of equations.
The substitution method is a full strategy for solving a system of equations. Substituting is the single move it is built on.
Quick check: 3 questions
Question 1 of 3
Which shows 7 − 2p after substituting p = −4?
Show answer and explanation
Answer: B.2p means 2 times p, so it becomes 2(−4), and the value is 7 + 8 = 15. The first choice lost the multiplication, 7 − 24 wrote the digits side by side, and 5p combined unlike terms instead of substituting.
Question 2 of 3
Which value of x is a solution of x2 − x = 12?
Show answer and explanation
Answer: D. Substitute each one: (−3)2 − (−3) = 9 + 3 = 12, so −3 works. x = 3 gives 6, x = 6 gives 30, and x = 12 gives 132. (The other solution is x = 4.)
Question 3 of 3
If b = 3a, which equation results from substituting into a + b = 24?
Show answer and explanation
Answer: A. Replace b with the expression 3a: a + 3a = 24, so a = 6. The second choice replaced a instead of b, the third dropped the a in 3a, and the last added letters that are not like terms.
Substitute: frequently asked questions
What is the difference between substitute and plug in?
There is none in math class. Plug in is the everyday way to say substitute: you put a value in where the variable was. Textbooks and tests use substitute, and it also covers putting a whole expression in place of a variable, as in replacing y with x + 4 when solving a system of equations.
How do you check an answer by substitution?
Put your answer back into the original equation and simplify each side separately. If the two sides are equal, the answer is correct. For 5x + 2 = 17, substituting x = 3 gives 15 + 2 = 17, a true statement. If the sides differ, look for an error in your solving steps.
Why do I need parentheses when I substitute?
Parentheses keep the replacement in one piece. They make multiplication visible, keep a negative sign attached to its number, and make an exponent apply to the whole value. Without them, x2 at x = −1 turns into −12 = −1 instead of the correct (−1)2 = 1.
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Zero itself is neither negative nor positive.Number System · Grade 6, Grade 7SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6ExponentAn exponent tells how many times to use a base as a factor. It is the small raised number to the upper right of the base: in 53, the base is 5 and the exponent is 3, so 53 = 5 × 5 × 5 = 125. Any nonzero number with an exponent of 0 equals 1.Algebra · Grade 6, Grade 7, Grade 8Like TermsLike terms have exactly the same variables raised to exactly the same powers; only their coefficients may differ. 3x and 8x are like terms, and so are 5a2 and −2a2, but 4x and 4y are not. 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