Question 1: Classify the system of equations and identify the number of solutions. 7x + 3y = 10 3y = 9 − 7x Answers: consistent, dependent; one inconsistent; one inconsistent; none consistent, dependent; infinite Question 2: Classify the system of equations and identify the number of solutions. 3x + y = 4 12x + 4y = 16 Answers: consistent, independent; one inconsistent; none consistent, dependent; one consistent, dependent; infinite Question 3: John and Harry went to a stationery shop. John bought 3 pens and 8 notebooks for $20.50. Harry bought 4 pens and 5 notebooks for $16.00. Identify the cost of a pen and the cost of a notebook. Answers: pen: $1.00; notebook: $2.50 pen: $2.00; notebook: $1.50 pen: $1.50; notebook: $2.00 pen: $2.00; notebook: $3.00

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31-07-2020
Mathematics

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Question 1: Classify the system of equations and identify the number of solutions. 7x + 3y = 10 3y = 9 − 7x Answers: consistent, dependent; one inconsistent; one inconsistent; none consistent, dependent; infinite Question 2: Classify the system of equations and identify the number of solutions. 3x + y = 4 12x + 4y = 16 Answers: consistent, independent; one inconsistent; none consistent, dependent; one consistent, dependent; infinite Question 3: John and Harry went to a stationery shop. John bought 3 pens and 8 notebooks for $20.50. Harry bought 4 pens and 5 notebooks for $16.00. Identify the cost of a pen and the cost of a notebook. Answers: pen: $1.00; notebook: $2.50 pen: $2.00; notebook: $1.50 pen: $1.50; notebook: $2.00 pen: $2.00; notebook: $3.00

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MrRoyal MrRoyal · Answer 1 · 2020-08-06T10:08:31+02:00

Answer:

1. The equations is inconsistent and has no solution

2. The equations is consistent and has no solution

3. A pen costs $1.50 and a notebook costs $2.00

Step-by-step explanation:

Solving [tex]7x + 3y = 10[/tex] and [tex]3y = 9 - 7x[/tex]

[tex]7x + 3y = 10[/tex] --- Equation 1

[tex]3y = 9 - 7x[/tex] --- Equation 2

Add 7x to both sides in equation 2

[tex]7x + 3y = 9 - 7x + 7x[/tex]

[tex]7x + 3y = 9[/tex] --- Equation 3

Subtract equation 3 from 1

[tex](7x + 3y = 10) - (7x + 3y = 9)[/tex]

[tex]7x - 7x + 3y - 3y = 10 - 9[/tex]

[tex]0 + 0 = 1[/tex]

[tex]0 \neq 1[/tex]

The equations is inconsistent and has no solution

Solving [tex]3x + y = 4[/tex] and [tex]12x + 4y = 16[/tex]

[tex]3x + y = 4[/tex] -- Equation 1

[tex]12x + 4y = 16[/tex] ---- Equation 2

Make y the subject of formula in equation 1

[tex]y = 4 - 3x[/tex]

Substitute 4 - 3x for y in equation 2

[tex]12x + 4(4 - 3x) = 16[/tex]

[tex]12x + 16 - 12x = 16[/tex]

Collect Like Terms

[tex]12x - 12x = 16 - 16[/tex]

[tex]0 = 0[/tex]

The equations is consistent and has no solution

3. Solving John and Harry

Given;

Represent Pen with P and Notes with N

John: [tex]3P + 8N = 20.5[/tex]

Harry: [tex]4P + 5N = 16.00[/tex]

Required

Find P and N

Make P the subject of formula in equation 2

[tex]4P = 16 - 5N[/tex]

[tex]P = \frac{16 - 5N}{4}[/tex]

Substitute [tex]P = \frac{16 - 5N}{4}[/tex] in equation 1

[tex]3P + 8N = 20.5[/tex]

[tex]3(\frac{16 - 5N}{4}) + 8N = 20.5[/tex]

Open the bracket

[tex]\frac{48 - 15N}{4} + 8N = 20.5[/tex]

Take LCM

[tex]\frac{48 - 15N + 32N}{4} = 20.5[/tex]

[tex]\frac{48 + 17N}{4} = 20.5[/tex]

Multiply both sides by 4

[tex]4 * \frac{48 + 17N}{4} = 20.5 * 4[/tex]

[tex]48 + 17N = 82[/tex]

Subtract 48 from both sides

[tex]48 - 48 + 17N = 82 - 48[/tex]

[tex]17N = 82 - 48[/tex]

[tex]17N = 34[/tex]

Divide both sides by 17

[tex]17N/17 = 34/17[/tex]

[tex]N = 34/17[/tex]

[tex]N = 2[/tex]

Substitute 2 for N in [tex]P = \frac{16 - 5N}{4}[/tex]

[tex]P = \frac{16 - 5 * 2}{4}[/tex]

[tex]P = \frac{16 - 10}{4}[/tex]

[tex]P = \frac{6}{4}[/tex]

[tex]P = 1.5[/tex]

Hence, a pen costs $1.50 and a notebook costs $2.00