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2 years ago

1. Is the following pair of linear equations consistent? Justify your answer.

Mathematics

2 answers:

qaws [65]2 years ago

5 0

<h3>Answer:</h3>

<u>Given equation</u>:– 2ax + by = a, 4ax + 2by - 2a = 0

a1 = 2a; b1 = b; c1 = - a & a2 = 4a; b2 = 2b; c2 = - 2a.

<u>For consistence, a1/a2 = b1/b2 = c1/c2 must be equal</u>

2a/4a = b/2b = -a/-2a
1/2 = 1/2 = 1/2

<u>So, The given equation is consistence</u>.

atroni [7]2 years ago

3 0

Yes.

<h3>Justification:</h3>

Here,

a1/a2 = 2a/4a = 1/2,
b1/b2 = b/2b = 1/2,
c1/c2 = - a/- 2a = 1/2.

∵ a1/a2 = b1/b2 = c1/c2

∴ <u>The given system of equations is consistent</u>.

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Lena [83]

Answer:

a.(10,23)

b.(7,30)

e.(20,20)

Step-by-step explanation:

We are given that

x=Width of garden

y=Length of garden

According to question

$x\geq 5$

$y\geq 20$

Perimeter of rectangle= $2(x+y)$

Where x=Width of rectangle

y=Length of rectangle

Fencing used = $2(x+y)$

$2(x+y)\leq 80$

First we change inequality into equality

$x=5$ ...(1)

$y=20$ ...(2)

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$x+y=40$ ...(3)

Substitute x=0 in equation (3)

$y=40$

Substitute y=0 in equation (3)

$x=40$

Substitute x=0 and y=0 in equation (3)

$2(x+y)\leq 80$

$0\leq 80$

It is true. Therefore, the shaded region below the line.

$0\geq 5$

$0\geq 20$

These are false equation .Therefore, the shaded region above the line.

Substitute x=5 in equation (3)

$5+y=40$

$y=40-5=35$

Substitute y=20 in equation (3)

$x+20=40$

$x=40-20=20$

Intersection point of equation (1) and (3) is (5,35) and intersect point of equation (2) and (3) is (20,20).

Now,

a.(10,23)

Substitute in

$2(x+y)\leq 80$

$2(10+23)\leq 80$

$66\geq 80$

10>5 and 23>20

it satisfied all inequality.

Hence, it is a solution.

b.(7,30)

7>5

30>20

$2(7+30)=74$

it satisfied all inequality.

Hence, it is a solution.

c.(18,25)

18>5

25>20

$2(18+25)=86>80$

It does not satisfied third inequality

Hence, it is not a solution.

d.(8,35)

8>5

35>20

$2(8+35)=86>80$

It does not satisfied third inequality

Hence, it is not a solution.

e.(20,20)

$2(20+20)=80$

20>5

20=20

it satisfied all inequality.

Hence, it is a solution.

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Answer:

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