Questions and Answers
What does substitution mean in Algebra?
Putting numbers where the letters are.
If x = 6, what is the value of x - 2?
4
When x = 2, what is the value of 10/x + 4?
9
When x = 5, what is the value of x + x/2?
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If x = 3 and y = 4, what is the value of x² + xy?
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If x = 3 (unknown y), what is the value of x² + xy?
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If x = -2, what is the value of 1 - x + x²?
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If x = 4, what is the value of 12/x + 3?
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If y = 10, what is the value of 5(y - 4)/2?
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If x = 2 and y = 3, what is the value of xy + y²?
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If x = 5 and y = 6, what is the value of 2x - 12/y?
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If x = 4 and y = 2, what is the value of x² + y³?
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If z = -3, what is the value of z² - z - 1?
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If y = -5, what is the value of 3y² + 7y - 4?
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If a = 6 and b = -2, what is (a - b) / (a + b)?
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If m = 4 and n = 3, what is (m² - n²) / (m² + n²)?
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If x = 4 and y = 12, what is 1/x + 1/y?
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Study Notes
Algebra Substitution Overview
- Substitution in algebra involves replacing variables (e.g., x) with given numerical values.
- For instance, if x=6 in the expression x − 2, it becomes 6 − 2 = 4.
Simple Examples of Substitution
- If x=2, substitute into 10/x + 4:
- 10/2 + 4 = 5 + 4 = 9.
- Substitute x=5 into x + x/2:
- 5 + 5/2 = 5 + 2.5 = 7.5.
- With x=3 and y=4, evaluate x^2 + xy:
- 3^2 + 3×4 = 9 + 12 = 21.
- With x=3 and unknown y, evaluate x^2 + xy:
- 3^2 + 3y = 9 + 3y (y remains unknown).
Negative Numbers in Substitution
- Use parentheses for negative numbers to ensure proper calculations.
- With x = −2 in 1 − x + x^2:
- 1 − (−2) + (−2)^2 = 1 + 2 + 4 = 7.
Rules for Operations
- Adding/Subtracting:
- Two like signs become positive; e.g., 3+(+2) = 5.
- Two unlike signs yield a negative; e.g., 7 + (−2) = 5.
- Multiplying/Dividing:
- Two like signs yield a positive; e.g., (−3) × (−2) = 6.
- Two unlike signs yield a negative; e.g., 3 × (−2) = −6.
Evaluating Expressions with Given Values
- If x=4, find 12/x + 3:
- 12/4 + 3 = 3 + 3 = 6.
- If y=10, evaluate 5(y-4)/2:
- 5(10-4)/2 = 5×6/2 = 30/2 = 15.
- With x=2 and y=3, calculate xy + y²:
- 2×3 + 3² = 6 + 9 = 15.
- With x=5 and y=6, evaluate 2x - 12/y:
- 2×5 - 12/6 = 10 - 2 = 8.
- If x=4 and y=2, evaluate x² + y³:
- (4×4) + (2×2×2) = 16 + 8 = 24.
- For z = -3, find z² - z - 1:
- (-3)² - (-3) - 1 = 9 + 3 - 1 = 11.
- If y = -5, evaluate 3y² + 7y - 4:
- 3×(-5)² + 7×(-5) - 4 = 75 - 35 - 4 = 36.
Fractional Evaluations
- If a=6 and b=-2, evaluate (a-b)/(a+b):
- (6-(-2))/(6+(-2)) = (6+2)/(6-2) = 8/4 = 2.
- For m=4 and n=3, find (m²-n²)/(m²+n²):
- (4²-3²)/(4²+3²) = (16-9)/(16+9) = 7/25.
- If x=4 and y=12, evaluate 1/x + 1/y:
- 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3.
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