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 + x2 + 5
|(x - 3)(3x + 2) = 3x2 - 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


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