4.1 求线性方程的解

求线性方程的三个解: y = 9 x + 2 .
请以有序数据对列表的形式提供答案,并用逗号分隔答案.

[1] [0]

任何由三个或更多有序数据对组成的集合,只要它们都是方程  y = 9 x + 2 的解,均被视为有效答案. 可能的答案包括:(0, 2), (1, 11), (–1, –7).

Step 1 of 4

We can substitute any value we want for x or any value for y . Since the equation is in y -form, it will be easier to substitute in values of x . Let’s pick x = 0 x = 1 x = - 1 .

Step 2 of 4

     x = 0                      x = 1                      x = - 1

     y = 9 x + 2          y = 9 x + 2          y = 9 x + 2

Substitute the value into the equation.
     y = 9 · 0 + 2          y = 9 · 1 + 2          y = 9 · - 1 + 2

Simplify.
     y = 0 + 2              y = 9 + 2                  y = - 9 + 2

Simplify.
     y = 2                      y = 11                          y = - 7

Write the ordered pair.
     ( 0 2 )                      ( 1 11 )                      ( - 1 - 7 )

Step 3 of 4

Check.
( 0 , 2 ) ( 1 , 11 ) ( - 1 , - 7 ) y = 9 x + 2 y = 9 x + 2 y = 9 x + 2 2 9 · 0 + 2 11 9 · 1 + 2 - 7 9 · - 1 + 2 2 0 + 2 11 9 + 2 - 7 - 9 + 2 2 = 2 11 = 11 - 7 = - 7

Step 4 of 4

So, ( 0 2 ) , ( 1 11 ) , ( - 1 - 7 ) are all solutions to y = 9 x + 2 .