BANK & INSURANCE (QUADRATIC EQUATION PART 3)

From I:
x² + x - 42 = 0
x² + 7x - 6x - 42 = 0
x(x + 7) - 6(x + 7) = 0
(x - 6)(x + 7) = 0
x = -7, 6

From II:
y² - 13y + 42 = 0
y² - 7y - 6y + 42 = 0
y(y - 7) - 6(y - 7) = 0
(y - 6)(y - 7) = 0
y = 6, 7

From I:
6x² - 7x + 2 = 0
6x² - 3x - 4x + 2 = 0
3x(2x - 1) - 2(2x - 1) = 0
(3x - 2)(2x - 1) = 0
x = 2/3, 1/2

From II:
30y² - 49y + 20 = 0
30y² - 25y - 24y + 20 = 0
5y(6y - 5) - 4(6y - 5) = 0
(5y - 4)(6y - 5) = 0
y = 4/5, 5/6

From I:
4x + 7y = 143
Multiplying both sides by 2, we get
8x + 14y = 286 ----(1)

From II:
8x + 2y = 130 ----(2)

Subtracting (2) from (1), we get
12y = 156
y = 13
So, x = 13

From I:
2x + 5y = 26
Multiplying both sides by 2, we get
4x + 10y = 52, which is equation II.
So, it cannot be solved.

From I:
x² + 29x + 210 = 0
x² + 15x + 14x + 210 = 0
x(x + 15) + 14(x + 15) = 0
(x + 14)(x + 15) = 0
x = -14, -15

From II:
y² + 35y + 300 = 0
y² + 15y + 20y + 300 = 0
y(y + 15) + 20(y + 15) = 0
(y + 15)(y + 20) = 0
y = -15, -20

From I:
x² - 22x + 120 = 0
x² - 12x - 10x + 120 = 0
x(x - 12) - 10(x - 12) = 0
(x - 12)(x - 10) = 0
x = 12, 10

From II:
y² - 23y + 132 = 0
y² - 11y - 12y + 132 = 0
y(y - 11) - 12(y - 11) = 0
(y - 11)(y - 12) = 0
y = 11, 12

From I:
6x² - 11x + 4 = 0
6x² - 3x - 8x + 4 = 0
3x(2x - 1) - 4(2x - 1) = 0
(3x - 4)(2x - 1) = 0
x = 4/3, 1/2

From II:
10y² - 41y + 40 = 0
10y² - 16y - 25y + 40 = 0
2y(5y - 8) - 5(5y - 8) = 0
(2y - 5)(5y - 8) = 0
y = 5/2, 8/5

From I:
9x + 3y = 57
3x + y = 19 -----(1)

From II:
2x + y = 14 -----(2)

Solving (1) and (2), we get
x = 5 and y = 4

From I:
x² + 19x + 84 = 0
x² + 12x + 7x + 84 = 0
x(x + 12) + 7(x + 12) = 0
(x + 12)(x + 7) = 0
x = -7, -12

From II:
y² - y - 56 = 0
y² - 8y + 7y - 56 = 0
y(y - 8) + 7(y - 8) = 0
(y - 8)(y + 7) = 0
y = -7, 8

From I:
0.2x + 0.4y = 1600
Multiplying both sides by 1.5, we get
0.3x + 0.6y = 2400, which is second equation.

we cannot determine a fixed relation between x and y