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jekas [21]
2 years ago
11

Use the substitution and to rewrite the equations in the system in terms of the variables and . Solve the system in terms of u a

nd v . Then back substitute to determine the solution set to the original system in terms of x and y.
-3/x+4/y=11
1/x-2/y=-5
Mathematics
1 answer:
Tatiana [17]2 years ago
4 0

Answer:

x = -1 and y = 1/2

Step-by-step explanation:

Let u = 1/x, and v = 1/y

Then the pair of equations

-3/x + 4/y = 11

1/x - 2/y = -5

Can be written as

-3u + 4v = 11 .................................(1)

u - 2v = -5......................................(2)

From (2)

u = 2v - 5 .......................................(3)

Substituting (3) into (1)

-3(2v - 5) + 4v = 11

-6v + 15 + 4v = 11

-6v + 4v = 11 - 15

-2v = -4

v = 4/2 = 2

Substituting this value of v in (3)

u = 2v - 5

u = 2(2) - 5

= 4 - 5

= -1

That is

u = -1, v = 2

Since u = 1/x, and v = 1/y, we have

1/x = -1

=> x = -1

And

1/y = 2

=> y = 1/2

Therefore

x = -1 and y = 1/2

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Answer:

(1) Commutative property

(2) Distributive property/Definition of addition

(3) Compatibility with addition/Existence of additive inverse/Modulative property

(4) Compatibility with multiplication/Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

Step-by-step explanation:

We proceed to solve algebraically and explain each step:

1) 4\cdot x +1 +x + 3 = -11 GIven

2) 4\cdot x +x +1 + 3 = -11 Commutative property

3) (4+1)\cdot x +4 = -11 Distributive property/Definition of addition

4) 5\cdot x +4 = -11 Definition of addition

5) 5\cdot x +4 -4 = -11-4 Compatibility with addition

6) 5\cdot x = -15 Existence of additive inverse/Modulative property

7) \frac{1}{5}\cdot (5\cdot x)= \frac{1}{5}\cdot (-15) Compatibility with multiplication

8) x = - 3 Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

Hence, we have the following answers:

(1) Commutative property

(2) Distributive property/Definition of addition

(3) Compatibility with addition/Existence of additive inverse/Modulative property

(4) Compatibility with multiplication/Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

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