基本方程 - 在线测验

以下测验提供与基本方程相关的多项选择题 (MCQ)。您需要阅读所有给定的答案，并点击正确的答案。如果您不确定答案，可以使用显示答案按钮检查答案。您可以使用下一测验按钮查看测验中的新一组问题。

Q 1 - 方程组 x/2+ y/9 = 11 和 x/3 + y/6 =9 的解为

答案：C

解释

The given equations are
9x+ 2y = 198...(i)
2x+y =54...(iii)
On multiplying (ii) by 2 and subtracting it from (i), we get: 5x= 90 ⇒x= 18
Putting x=18 in (ii), we get: 36+y = 54 ⇒y = 18
∴x = 18, y= 18

Q 2 - 解方程组 4/x+5y=7 和 3/x+4y =5，我们得到

答案：C

解释

Given equations are 4/x+5 y= 7 ...(i)
3/x+4y = 5  ...(ii)
On multiplying (i) by 3, (ii) by 4 and subtracting, we get -y =1 ⇒y= -1
Putting y= -1 in (i), we get 4/x-5 = 7 ⇒4/x= 12 ⇒12x= 4 ⇒x= 1/3
∴x= 1/3, y= -1

Q 3 - 如果 (5, ℏ) 是 2x+y-6 =0 的一个解，那么 ℏ=?

答案：A

解释

Clearly x= 5 and y= ℏ satisfies 2x+y- 6 = 0
∴ 2*5+ ℏ-6= 0 ⇒ 10+ℏ- 6= 0 ⇒ℏ+4= 0 ⇒ ℏ= -4

Q 4 - 如果 x/4 + y/3= 5/12 和 x/2+ y =1，那么 (x+y) 的估计值为

答案：C

解释

Given equations are 3x+4y= 5 ...(i) and x+2y =2 ...(ii)
On multiplying (ii) by 3 and subtracting (i) from it, we get 2y = 1 ⇒y = 1/2
Putting y = 1/2 in (ii), we get x+2*1/2 = 2 ⇒x+1= 2 ⇒x =1
∴(x+y ) = (1+1/2 ) = 3/2

Q 5 - 如果 2a+3 b= 17 和 2a+2-3b+1= 5 那么

答案：D

解释

Given equation are  2a +3b = 17 ...(i)
2a*2²- 3b*3ⁱ= 5   ⇒4*2a- 3*3b= 5 ...(ii)
Putting 2a = x and 3b= y, we get:
x+y= 17 ...(iii)     4x-3y = 5...(iv)
Multiplying (iii) by 3 and adding (iv) to it, we get: 7x= 56
⇒x= 8
Putting x= 8 in (iii), we get: 8+ y = 17 ⇒y = 9
∴ (2a= 8 = 2³ ⇒a = 3) and (3b= 9= 3² ⇒b= 2)
∴ a= 3, b= 2

Q 6 - 如果 4x+6y =32 和 4x-2y= 4，那么 8y =?

答案：D

解释

4x+6y = 32...(i) 4x-2y = 4...(ii)
On subtracting (ii) from (i), we get: 8 y= 28

Q 7 - 方程组 2x+3y=2 和 3x+2y =2 的解可以用坐标平面上的一个点表示在

答案：A

解释

2x+3y = 2...(i) , 3x+2y= 2...(ii)
Multiplying (i) by 2 and (ii) by 3 and subtracting, we get: -5x= -2 ⇒x= 2/5
Putting x= 2/5 in (i), we get 4/5+3y= 2 ⇒3y = (2-4/5) = 6/5 ⇒y = 6/5*1/3 =2/5
∴ the solution can be represented by a point (2/5, 2/5) which lies in 1st quadrant.

Q 8 - 方程组 2x+ℏy= 11 和 5x-7y = 5 无解时

答案：C

解释

For no solution , we have a₁/a₂ = b₁/b₂ ≠c₁/c₂
i.e. 2/5 = ℏ/-7 ≠11/5 ⇒ℏ= -14/5

Q 9 - 方程组 x+2y = 3 和 2x+ 4y = 3 的解有

答案：B

解释

Here a₁/a₂= 1/2, b₁/b₂=2/4=1/2 and c₁/c₂=3/3=1.
∴ a₁/a₂=b₁/b₂≠c₁/c₂.
∴Give system has no solution.

Q 10 - 如果 3x-5y = 5 和 x/x+y = 5/7，那么 (x-y) =?

答案：A

解释

3x -5y=5 ...(i), 7x=5x+5y⇒2x-5y=0 ...(ii)
On subtracting (ii) from (i), we get=5.
3*5-5y=5⇒5y=10⇒y=2.
∴(x-y) = (5-2) =3.

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