72.1k views
1 vote
Solve The following equations(i) -5x + 3y = 51 y = 10x - 8(ii) 6x + y = -10 5x + y = -10(iii) 2x - y = 32 y - 5x = 13(iv) 3x -y = 7 x - 2y = 4

User Elinore
by
8.2k points

1 Answer

5 votes

Given:

Some equations are given as below

(i) -5x + 3y = 51

y = 10x - 8

(ii) 6x + y = -10

5x + y = -10

(iii) 2x - y = 32

y - 5x = 13

(iv) 3x -y = 7

x - 2y = 4

Find:

we have to solve these equations.

Step-by-step explanation:

(i) -5x + 3y = 51 ....................(1)

y = 10x - 8........................(2)

put y = 10x - 8 in eqn (1), we get

-5x + 3(10x - 8) = 51

-5x + 30x - 24 = 51

25x = 51 + 24

25x = 75

x = 75/25

x = 3

put x = 3 in eqn (2), we get

y = 10(3) - 8 = 30 - 8 = 22

Therefore, x = 3 and y = 22

answer is (3, 22)

...................................................................................................

(ii) 6x + y = -10........................(3)

5x + y = -10..........................(4)

subtract eqn(4) from eqn(3), we get

6x - 5x = 0

x = 0

put x = 0 in eqn(3). we get

6(0) + y = -10

y = -10

Therefore, x = 0, y = -10

Answer is (0, -10)

.................................................................................................

(iii) 2x - y = 32........................(5)

y - 5x = 13..........................(6)

add eqn(5) and eqn(6), we get

2x -y + y - 5x = 32 + 13

-3x = 45

x = -45/3

x = -15

put x = -15 in eqn(5), we get

2(-15) - y = 32

-30 - y = 32

-y = 32 + 30

y = -62

Therefore, x = -15. y = -62

Answer is (-15, -62)

.........................................................................................................

(iv) 3x -y = 7..............................(7)

x - 2y = 4.............................(8)

Multiply eqn(8) by 3 and subtract from eqn (7) as following

3x - y = 7

3x - 6y = 12

- + -

.....................

5y = -5

y = -1

put y = -1 in eqn(7), we get

3x - (-1) = 7

3x + 1 = 7

3x = 7 - 1

3x = 6

x = 6/3

x = 2

Therefore, x = 2 and y = -1

Answer is (-1, 2)

....................................................................................................

User GHad
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories