1. 解方程组:
5x + 3y = 348
3x + 2y = 216
首先,将第一个方程乘以3,第二个方程乘以5,得到:
15x + 9y = 1044
15x + 10y = 1080
接着,将第二个方程减去第一个方程,得到:
10y - 9y = 1080 - 1044
y = 36
将y = 36代入第一个方程:
5x + 3(36) = 348
5x + 108 = 348
5x = 240
x = 48
因此,原方程的解为 x = 48, y = 36。
2. 解方程:
7(2x + 1) = 49
将等式两边同时除以7:
2x + 1 = 7
2x = 6
x = 3
3. 解方程:
(x + 8) ÷ 8 = 6
将等式两边同时乘以8:
x + 8 = 48
x = 40
4. 解方程:
4(x + 3) = 32 × 3
x + 3 = 32 × 3 / 4
x + 3 = 24
x = 21
5. 解方程:
3(x + 5) - 42 = 12
3(x + 5) = 12 + 42
x + 5 = 54 / 3
x + 5 = 18
x = 13
6. 解方程:
(10x - 90 + 2x) ÷ 2 = 75
将等式两边同时乘以2:
10x - 90 + 2x = 150
12x = 240
x = 20
7. 解方程:
(7x - 3x + 59) ÷ 3 = 29
将等式两边同时乘以3:
7x - 3x + 59 = 87
4x + 59 = 87
4x = 28
x = 7
8. 解方程:
9x - 8 = x
将x项移到等式一边:
9x - x = 8
8x = 8
x = 1
9. 解方程:
12x + 12 = 16x
将x项移到等式一边:
12x - 16x = -12
-4x = -12
x = 3
10. 解方程:
144 ÷ x + 6 = 12
将等式两边同时减去6:
144 ÷ x = 12 - 6
144 ÷ x = 6
x = 144 ÷ 6
x = 24