Systems, absolute value and scientific notation

The three Algebra 1 strands that come after quadratics: solving a pair of equations, equations inside absolute-value bars, and arithmetic in scientific notation.

6 sheets · 48 questions · one answer key · 7 pages

Recommended for grades 8–9

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By elimination Sheet 1 of 6

Systems of equationsBy elimination

Name: Date:

Solve each pair by adding the two equations.

1−2x + 12y = −30x − 12y = 15

25x + 2y = −128x − 2y = 38

38x + 8y = −56−5x − 8y = 20

46x + 9y = 364x − 9y = −36

5−5x + 8y = −606x − 8y = 56

6x + 2y = 611x − 2y = 18

76x + 6y = 422x − 6y = −34

8−3x + 2y = 47x − 2y = 12

Systems of equationsBy substitution

Name: Date:

Solve each pair by substitution.

1y = −x + 85x − 2y = −37

2y = 2x + 13−6x + 7y = −5

3y = 3x − 18−x + 9y = −6

4y = x − 72x + 2y = 34

5y = 3x − 18−12x + 7y = −36

6y = 3x + 110x − 2y = −2

7y = 4x + 8−12x + 3y = 24

8y = x + 156x + 2y = 30

Absolute value equationsSolve |x + b| = c

Name: Date:

Solve each equation. Each has two answers.

1|x − 4| = 6

2|x − 6| = 4

3|x + 4| = 4

4|x − 6| = 8

5|x − 1| = 6

6|x + 3| = 4

7|x| = 7

8|x + 1| = 4

Absolute value equationsSolve |ax + b| = c

Name: Date:

Solve each equation. Each has two answers.

1|3x − 6| = 6

2|3x − 3| = 21

3|2x − 8| = 2

4|3x − 6| = 9

5|2x − 4| = 4

6|2x + 2| = 2

7|3x − 9| = 12

8|2x + 4| = 6

Scientific notationMultiplying

Name: Date:

Multiply. Write each answer in scientific notation.

1(5 × 10−1) × (8 × 10−3)

2(6 × 106) × (8 × 10−5)

3(4 × 106) × (2 × 105)

4(3 × 107) × (6 × 102)

5(3 × 10−4) × (1.5 × 108)

6(5 × 104) × (8 × 10−4)

7(3 × 10−2) × (1.5 × 107)

8(2 × 10−1) × (2 × 103)

Scientific notationDividing

Name: Date:

Divide. Write each answer in scientific notation.

1(7.5 × 107) ÷ (3 × 10−2)

2(2 × 103) ÷ (2.5 × 108)

3(3 × 10−4) ÷ (1.5 × 108)

4(6 × 104) ÷ (3 × 102)

5(4.5 × 107) ÷ (7.5 × 10−3)

6(6 × 108) ÷ (4 × 104)

7(1.2 × 103) ÷ (1.5 × 105)

8(4.5 × 104) ÷ (7.5 × 107)

Power Pack · Systems, absolute value and scientific notationAnswer key

By elimination

1. −2x + 12y = −30, x − 12y = 15 → (15, 0)2. 5x + 2y = −12, 8x − 2y = 38 → (2, −11)3. 8x + 8y = −56, −5x − 8y = 20 → (−12, 5)4. 6x + 9y = 36, 4x − 9y = −36 → (0, 4)5. −5x + 8y = −60, 6x − 8y = 56 → (−4, −10)6. x + 2y = 6, 11x − 2y = 18 → (2, 2)7. 6x + 6y = 42, 2x − 6y = −34 → (1, 6)8. −3x + 2y = 4, 7x − 2y = 12 → (4, 8)

By substitution

1. y = −x + 8, 5x − 2y = −37 → (−3, 11)2. y = 2x + 13, −6x + 7y = −5 → (−12, −11)3. y = 3x − 18, −x + 9y = −6 → (6, 0)4. y = x − 7, 2x + 2y = 34 → (12, 5)5. y = 3x − 18, −12x + 7y = −36 → (10, 12)6. y = 3x + 1, 10x − 2y = −2 → (0, 1)7. y = 4x + 8, −12x + 3y = 24 → (1, 12)8. y = x + 15, 6x + 2y = 30 → (0, 15)

|x + b| = c

1. |x − 4| = 6 → x = −2 or x = 102. |x − 6| = 4 → x = 2 or x = 103. |x + 4| = 4 → x = −8 or x = 04. |x − 6| = 8 → x = −2 or x = 145. |x − 1| = 6 → x = −5 or x = 76. |x + 3| = 4 → x = −7 or x = 17. |x| = 7 → x = −7 or x = 78. |x + 1| = 4 → x = −5 or x = 3

|ax + b| = c

1. |3x − 6| = 6 → x = 0 or x = 42. |3x − 3| = 21 → x = −6 or x = 83. |2x − 8| = 2 → x = 3 or x = 54. |3x − 6| = 9 → x = −1 or x = 55. |2x − 4| = 4 → x = 0 or x = 46. |2x + 2| = 2 → x = −2 or x = 07. |3x − 9| = 12 → x = −1 or x = 78. |2x + 4| = 6 → x = −5 or x = 1

Multiplying in scientific notation

1. (5 × 10⁻¹) × (8 × 10⁻³) = 4 × 10⁻³2. (6 × 10⁶) × (8 × 10⁻⁵) = 4.8 × 10²3. (4 × 10⁶) × (2 × 10⁵) = 8 × 10¹¹4. (3 × 10⁷) × (6 × 10²) = 1.8 × 10¹⁰5. (3 × 10⁻⁴) × (1.5 × 10⁸) = 4.5 × 10⁴6. (5 × 10⁴) × (8 × 10⁻⁴) = 4 × 10¹7. (3 × 10⁻²) × (1.5 × 10⁷) = 4.5 × 10⁵8. (2 × 10⁻¹) × (2 × 10³) = 4 × 10²

Dividing in scientific notation

1. (7.5 × 10⁷) ÷ (3 × 10⁻²) = 2.5 × 10⁹2. (2 × 10³) ÷ (2.5 × 10⁸) = 8 × 10⁻⁶3. (3 × 10⁻⁴) ÷ (1.5 × 10⁸) = 2 × 10⁻¹²4. (6 × 10⁴) ÷ (3 × 10²) = 2 × 10²5. (4.5 × 10⁷) ÷ (7.5 × 10⁻³) = 6 × 10⁹6. (6 × 10⁸) ÷ (4 × 10⁴) = 1.5 × 10⁴7. (1.2 × 10³) ÷ (1.5 × 10⁵) = 8 × 10⁻³8. (4.5 × 10⁴) ÷ (7.5 × 10⁷) = 6 × 10⁻⁴

Systems, absolute value and scientific notation

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The algebra track

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