解决以下方程组：
问题1. 11x + 15y + 23 = 0和7x – 2y – 20 = 0
解决方案：
11x +15y + 23 = 0 …………………………. (i)
7x – 2y – 20 = 0 …………………………….. (ii)
From (ii)
2y = 7x – 20
⇒ y = (7x −20)/2 ……………………………… (iii)
Putting y in (i) we get,
⇒ 11x + 15((7x−20) / 2) + 23 = 0
⇒ 11x + (105x − 300) / 2 + 23 = 0
Taking 2 as LCM
⇒ (22x + 105x – 300 + 46) = 0
⇒ 127x – 254 = 0
⇒ x = 2
Putting x in (iii)
⇒ y = (7(2) − 20)/2
⇒ y= -3
Therefore, x = 2 and y = -3
问题2。3x– 7y + 10 = 0和y – 2x – 3 = 0
解决方案：
3x – 7y + 10 = 0 …………………………. (i)
y – 2x – 3 = 0 ……………………………….. (ii)
From (ii)
y – 2x – 3 = 0
y = 2x+3 ……………………………… (iii)
Substituting y in (i)
⇒ 3x – 7(2x+3) + 10 = 0
⇒ 3x – 14x – 21 + 10 = 0
⇒ -11x = 11
⇒ x = -1
Putting x in (iii)
⇒ y = 2(-1) + 3
⇒ y= 1
Therefore, x = -1 and y =1
问题3. 0.4x + 0.3y = 1.7和0.7x – 0.2y = 0.8
解决方案：
0.4x + 0.3y = 1.7
0.7x – 0.2y = 0.8
Multiply LHS and RHS by 10
4x + 3y = 17 ……………………….. (i)
7x – 2y = 8 …………………………… (ii)
From (ii)
7x – 2y = 8
⇒ x = (8 + 2y) / 7……………………………… (iii)
Substituting x (i)
⇒ 4[(8 + 2y) / 7] + 3y = 17
Taking 7 as LCM
⇒ 32 + 8y + 21y = (17 × 7)
⇒ 29y = 87
⇒ y = 3
Putting y in (iii)
⇒ x = (8 + 2(3)) / 7
⇒ x = 14/7
⇒ x = 2
Therefore, x = 2 and y = 3
问题4. x / 2 + y = 0.8和7 /(x + y / 2)= 10
解决方案：
x/2 + y = 0.8
Taking 2 as LCM
⇒ x + 2y = 1.6…… (i)
7/(x + y/2) = 10
⇒7 = 10(x + y/2)
⇒7 = 10x + 5y
Multiply (i) by 10
10x + 20y = 16 ……………………….. (ii)
10x + 5y = 7 …………………………… (iii)
(ii) – (iii)
⇒ 15y = 9
⇒ y = 3/5
Putting y in (ii)
x = [16 − 20(3/5)] / 10
⇒ (16 – 12) / 10 = 4/10
⇒ x = 2/5
Therefore, x = 2/5 and y = 3/5
问题5. 7(y + 3)– 2(x + 2)= 14和4(y – 2)+ 3(x – 3)= 2
解决方案：
7(y + 3) – 2(x + 2) = 14…………………………. (i)
4(y – 2) + 3(x – 3) = 2……………………………….. (ii)
From (i)
⇒ 7y + 21 – 2x – 4 = 14
⇒ 7y = 14 + 4 – 21 + 2x
⇒ y = (2x – 3) / 7
From (ii)
⇒ 4y – 8 + 3x – 9 = 2
⇒ 4y + 3x – 17 – 2 = 0
⇒ 4y + 3x – 19 = 0 …………….. (iii)
Substituting y in (iii)
4[(2x − 3)/7] + 3x – 19=0
Taking 7 as LCM
⇒ 8x – 12 + 21x – (19 × 17) = 0
⇒ 29x = 145
⇒ x = 5
Putting x and in (iii)
⇒ 4y + 15 -19 = 0
⇒ 4y — 4 = 0
⇒ 4y = 4
⇒ y = 1
Therefore, x = 5 and y = 1
问题6. x / 7 + y / 3 = 5和x / 2 – y / 9 = 6
解决方案：
x/7 + y/3 = 5…………………………. (i)
x/2 – y/9 = 6………………………………..(ii)
From (i)
Taking 21 as LCM
x/7 + y/3 = 5
⇒3x + 7y = (5×21)
⇒ 3x =105 – 7y
⇒ x = (105 – 7y) / 3……. (iii)
From (ii)
x/2 – y/9 = 6
Taking 18 as LCM
⇒ 9x – 2y = 108 ……………………… (iv)
Substituting x in (iv)
9[(105 − 7y) / 3] – 2y = 108
Taking 3 as LCM
⇒ 945 – 63y – 6y = 324
⇒ 945 – 324 = 69y
⇒ 69y = 621
⇒ y = 9
Putting y in (iv)
x = (105 − 7(9))/3
⇒ x = (105 − 63)/3 = 42/3
⇒ x = 14
Therefore, x = 14 and y = 9
问题7. x / 3 + y / 4 = 11和5x / 6 − y / 3 = -7
解决方案：
x/3 + y/4 = 11…………………………. (i)
5x/6 − y/3 = −7……………………………….. (ii)
From (i)
x/3 + y/4 = 11
Taking 12 as LCM
⇒ 4x + 3y = (11×12)
⇒ 4x =132 – 3y
⇒ x = (132 – 3y)/4……. (iii)
From (ii)
5x/6 − y/3 = −7
Takin 6 as LCM
⇒ 5x – 2y = -42 ……………………… (iv)
Substituting x in equation (iv)
⇒ 5[(132 − 3y) / 4] – 2y = -42
Taking 4 as LCM
⇒ 660 – 15y – 8y = -42 x 4
⇒ 660 + 168 = 23y
⇒ 23y = 828
⇒ y = 36
Putting y in (iii)
x = (132 – 3(36))/4
⇒ x = (132 − 108)/4 = 24/4
⇒ x = 6
Therefore, the x = 6 and y = 36
问题8. 4 / x + 3y = 8和6 / x-4y = -5
解决方案：
Taking 1/x = u
4u + 3y = 8…………………… (i)
6u – 4y = -5……………………. (ii)
From (i)
4u = 8 – 3y
⇒ u = (8 − 3y) / 4 …….. (iii)
Substituting u in (ii)
[6(8 − 3y) / 4] – 4y = -5
⇒ [3(8−3y)/2] − 4y = −5
Taking 2 as LCM
⇒ 24 − 9y −8y = −5 × 2
⇒ 24 – 17y = -10
⇒ -17y =- 34
⇒ y = 2
Putting y=2 in (iii)
u = (8 − 3(2)) / 4
⇒ u = (8 − 6)/4
⇒ u = 2/4 = 1/2
⇒ x = 1/u = 2
⇒ x = 2
Therefore, x = 2 and y = 2.
问题9. x + y / 2 = 4和2y + x / 3 = 5
解决方案：
x + y/2 = 4 ……………………. (i)
2y + x/3 = 5……………………. (ii)
From (i)
x + y/2 = 4
Taking 2 as LCM
⇒ 2x + y = 8
⇒ y = 8 – 2x …..(iii)
From (ii)
Taking 3 as LCM
x + 6y = 15 ……………… (iv)
Substituting y in (iii)
⇒ x + 6(8 – 2x) = 15
⇒ x + 48 – 12x = 15
⇒ -11x = 15 – 48
⇒ -11x = -33
⇒ x = 3
Putting x = 3 in (iii)
y = 8 – (2×3)
⇒ y = 8 – 6 = 2
Therefore, x = 3 and y = 2
问题10. x + 2y = 3/2和2x + y = 3/2
解决方案：
x + 2y = 3/2 …………………. (i)
2x + y = 3/2…………………… (ii)
Multiplying (i) by 4
⇒ 4x + 8y = 6 ………………………. (iii)
Multiplying (ii) by 2
4x + 2y = 3 ……………………………………………………. (iv)
Subtracting (iv) from (iii)
⇒ 6y = 3
⇒ y = 3/6
⇒ y = 1/2
Putting y = 1/2 in (iv)
⇒ 4x + 2(1/2) = 3
⇒ 4x + 1 = 3
⇒ 4x = 2
⇒ x = 2/4 = 1/2
Therefore, x = 1/2 and y = 1/2
问题11.√2x–√3y= 0和√3x−√8y= 0
解决方案：
√2x – √3y = 0……………………….. (i)
√3x − √8y = 0……………………….. (ii)
By substitution
√2x = √3y
By transposing
x = √(3/2)y ……………..(iii)
Substituting x in (ii)
√3x − √8y = 0
⇒ √3(√(3/2)y) − √8y = 0
⇒ (3/√2)y – √8y = 0
Taking √2 as the LCM
⇒ 3y – 4y = 0
⇒ -y = 0
⇒ y = 0
Putting the value of y in (iii)
⇒ x = 0
Therefore, x = 0 and y = 0
问题12. 3x –(y + 7)/ 11 + 2 = 10和2y +(x + 11)/ 7 = 10
解决方案：
3x – (y + 7)/11 + 2 = 10……………….. (i)
2y + (x + 11)/7 = 10…………………….. (ii)
By taking 11 as LCM in (i)
33x – y – 7 + 22 = (10 × 11)
⇒ 33x – y + 15 = 110
⇒ 33x + 15 – 110 = y
⇒ y = 33x – 95………. (iii)
By taking 7 as LCM in (ii)
14y + x + 11 = (10 × 7)
⇒ 14y + x + 11 = 70
⇒ 14y + x = 70 – 11
⇒ 14y + x = 59 …………………….. (iv)
Substituting (iii) in (iv)
14 (33x – 95) + x = 59
⇒ 462x – 1330 + x = 59
⇒ 463x = 1389
Transposing 463
⇒ x = 3
Putting x = 3 in (iii)
⇒ y = 33(3) – 95
⇒ y = 99 – 95
Therefore, y= 4
Therefore, x = 3 and y = 4
问题13。2x –(3 / y)= 9，3x +(7 / y)= 2，y ≠ 0
解决方案：
2x – (3/y) = 9……………………………. (i)
3x + (7/y) = 2…………………………… (ii)
Substituting 1/y = u
2x – 3u = 9 ………………………..(iii)
3x + 7u = 2………………………..(iv)
From (iii)
2x = 9 + 3u
⇒ x = (9+3u) / 2
Substituting the value of x in (iv)
3[(9 + 3u)/2] + 7u = 2
Taking 2 as LCM
⇒ 27 + 9u + 14u = (2 x 2)
⇒ 27 + 23u = 4
Transposing 27
⇒ 23u = -23
Transposing 23
⇒ u = -1
y = 1/u = -1
Putting u = -1 in (iii)
⇒ x = (9 + 3(-1)) / 2
⇒ x = 6/2
⇒ x = 3
Therefore, x = 3 and y = -1