# Systems of Equations - Problems & Answers

**Problem 1** Two of the following systems of equations have solution (1;3). Find them out by checking.

a)

|x + y = 5

|2x - y = 7;

b)

|2x + y = 5

|x - y = 2

c)

|3x + y = 6

|4x - 3y = -5

d)

|1/(x - 1) = y - 3

|x - y = -2

e)

|(9x + 4y)/3 - (5x - 11)/2 = 13 - y

|13x - 7y = -8

Answer: **c** and **e** has solution (1; 3)

**Problem 2** Are the systems equivalent(check if solutions of the both systems are the same):

|4x + 5y = 11

|x - y = 5

and

|4x - 5y = 11

|2x + y = 9 ?

Answer: No.

**(3-32)** Solve the system of equations:

**Problem 3**

|2y - x = -5

|y = 1 - 3x

Answer: x = 1, y = -2.

**Problem 4**

|3x - y = 13

|3y - 2x = -4

Answer: x = 5, y = 2.

**Problem 5**

|6x - y = 11

|12x - 2y - 22 = 0

Answer: The solution is every couple of numbers, which is solution of the equation 6x - y = 11.

**Problem 6**

|5u - 6v = -2

|7u + 18v = 2

Answer: x = -1, y = 1/2.

**Problem 7**

|8x - 5y + 16 = 0

|1x + 3y - 17 = 0

Answer: x = 1/2, y = 4.

**Problem 8**

|4(x + 2) - 7(x - y) = 7

|7(x + y) + 10(x - 2) = 79

Answer: x = 5, y = 2.

**Problem 9**

|3x + 4(x - 3) = 3(2y - 3) - 3y

|3y + 2(x - 4) = 5(y + 2) - 28

Answer: (-4; 1).

**Problem 10**

|(x + 3)(x - 1) = 4y + x^{2} + 5

|(x - 3)(3x + 2) = 3x^{2} - 14y + 15

Answer: There's no solution.

**Problem 11**

|(x - 1)(y + 2) - (x - 2)(y + 5) = 0

|(x + 4)(y - 3) - (x + 7)(y - 4) = 0

Answer: x = 5, y = 7.

**Problem 12**

|(x + 2)^{2} - (x + 3)(x - 3) - 3(y + 5) = 0

|(2y - 3)^{2} - y(4y - 3) + 12x - 15 = 0

Answer: The solution is every couple, which is solution to the equation 4x - 3y - 2 = 0.

**Problem 13**

|(y + 2)/6 - (y - 4)/2 = x/3

|(4/3)(y - 1) - 2x = -2

Answer: x = 3, y = 4.

**Problem 14**

|0.25x - 0.04y = 1

|0.4x + 1.5y = 40.7

Answer: x = 8, y = 25.

**Problem 15**

|(5x - 3y)/4 = (x - 5y)/3

|7x + y = 12

Answer: x = 2, y = -2

**Problem 16**

|(3x + 1)/5 + 2y -3 = 0

|(4y - 5)/6 + 3y - 9 = -1/2

Answer: x = -42/11, y = 28/11

**Problem 17**

|(3x - 1)/5 + 3y - 4 = 15

|(3y - 5)/6 + 2x - 8 = 23/3

Answer: x = 7, y = 5

**Problem 18**

|(2x - z)/6 + (2x - z)/9 = 3

|(x + z)/3 - (x - z)/4 = 4

Answer: x = y = 6

**Problem 19**

|(x - 1)/3 + (5y + 1)/2 = (x + 10y - 8)/6

|(x + 2)(5y - 2)/2 = 5 + 5xy/2 - 2(x + 1)

Answer: There's no solution.

**Problem 20**

|(5x - 1)/6 + (3y - 1)/10 = 3

|(11 - x)/6 + (11 + y)/4 = 3

Answer: x = 5, y = -3.

**Problem 21**

|y - 0.2(x - 2) = 1.4

|5/2 - (2y - 3)/4 = (4x - y)/8

Answer: x = 5, y = 2.

**Problem 22**

|x/5 + 0.03(10y - 20) = 0.8

|(2x + 4.5)/20 - 0.75 = (y - 3)/8

Answer: x = 4, y = 2.

**Problem 23**

|y - x - (5x - 4)/2 = 3 - (11y + 17)/4

|x + (9y + 11)/4 - (3y + 4)/7 = 6

Answer: x = 2, y = 1.

**Problem 24**

|(5x - 3y)/3 - (2y - 3x)/5 = x + 1

|(2x - 3y)/3 - (3y - 4x)/2 = y + 1

Answer: x = 3, y = 2.

**Problem 25**

|(x - 1)/4 (1 + y)/2 = 1/6 - (x + 2y)/6

|(x - 2)/3 + x/15 = (y + 4)/5 - (4x - y)/15

Answer: The solution is every couple, which is solution of the equation 5x - 2y = 11.

**Problem 26**

|(x + 2y)/4 - (x - 2y)/2 = 1 - [x - (7 - 2y)/3]

|3x - 2y = 8

Answer: x = 3, y = 1/2.

**Problem 27**

|(7 + x)/5 - (2x - y)/4 - 3y = -5

|(5y - 7)/2 + (4x - 3)/6 - 18 = -5x

Answer: x = 3, y = 2.

**Problem 28**

|11y/20 - 0.8(x/4 + 2.5) = 5/2

|(6x - 0.3y)/2 - 3/2 = 2(1 + x)

Answer: x = 5, y = 10.

**Problem 29**

|0.5x - (y - 4)/5 = 0.3x - (y - 4)/2

|0.5y - (x - 4)/6 = 7y/12 - (x - 3)/3

Answer: x = 3, y = 2.

**Problem 30**

|2(x - y)/3 + 1.6 = 8x/15 - (3y - 10)/5

|(3x + 4)/4 + y/8 = 5x/6 - (y - 17)/12

Answer: x = 5, y = 4.

**Problem 31**

|(2 + x)(5y - 2)/2 = 5 + 5xy/2 - 2(1 + x)

|(x - 1)^{2} + (2y + 1)^{2} = 2(1 + 2y)(x - 1)

Answer: The solution is every couple, which is solution of the equation x + 5y = 5