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

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 and

--- Equation 1

--- Equation 2

Add 7x to both sides in equation 2

 --- Equation 3

Subtract equation 3 from 1

The equations is inconsistent and has no solution

Solving and  

-- Equation 1

---- Equation 2

Make y the subject of formula in equation 1

Substitute 4 - 3x for y in equation 2

Collect Like Terms

The equations is consistent and has no solution

3. Solving John and Harry

Given;

Represent Pen with P and Notes with N

John:

Harry:

Required

Find P and N

Make P the subject of formula in equation 2

Substitute in equation 1

Open the bracket

Take LCM

Multiply both sides by 4

Subtract 48 from both sides

Divide both sides by 17

Substitute 2 for N in

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

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.