Question

read each problem carefully and solve as required then answer the questions that follow.​

Answer 1

Step-by-step explanation:

1)X+Y=6 and 3X+Y=10

2) No. of jeans =2

No. of blouses =4

3)Given system of linear equations in two variables are consistent and independent or Intersecting lines

Explanation:-

Given equations are

X+Y=6

=>X+Y-6=0

we have a1=1; b1=1; C1=-6

and

3X+Y=10

=>3X+Y-10=0

we have a2=3;b2=1;C2=-10

now

a1/a2=1/3

b1/b2=1/1=1

C1/C2=-6/-10=3/5

a1/a2≠b1/b2≠c1/c2

Given system of linear equations in two variables are consistent and independent or Intersecting lines

Answer 2

Answer:

Answer 1.

$\bf \:300x + 100y = 1000$

$\bf \:x + y = 6$

where,

• x = number of jeans purchased
• y = number of blouses purchased be 'y'.

Answer 2.

$\bf \:2 \: jeans \: and \: 4 \: blouses \: are \: purchased.$

Answer 3.

Let us consider 2 linear equations

$\bf \:a_1x + b_1y + c_1 = 0 \:and \: a_2x + b_2y + c_2 = 0$

then

1. System of equation is consistent and independent iff

$\bf \:\dfrac{a_1}{a_2} ≠\dfrac{b_1}{b_2}$

2. System of equation is consistent and dependent iff

$\bf \:\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$

3. System of equation is inconsistent iff

$\bf \:\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} ≠ \dfrac{c_1}{c_2}$

The solution of given equations is consistent and independent.

Step-by-step explanation:

Let number of jeans purchased be 'x' and number of blouses purchased be 'y'.

Case 1.

The cost price of 1 jean is Php 300 and cost price of 1 blose is Php 100. Total amount spend is Php 1000.

$\bf\implies \:300x + 100y = 1000....(1)$

Case 2.

Total number of jeans and blouse purchased is 6.

$\bf\implies \:x + y = 6$

$\bf\implies \:y = 6 - x.....(2)$

On substituting the value of y from (2) to (1), we get

$\bf\implies \:300x + 100(6 - x) = 1000$

$\bf\implies \:300x + 600 - 100x = 1000$

$\bf\implies \:200x = 1000 - 600$

$\bf\implies \:200x = 400$

$\bf\implies \:x = 2$

Put x = 2, in equation (2), we get

$\bf\implies \:y = 6 - 2 = 4$

So, it means 2 jeans and 4 blouses are purchased.