__The phrase__

*a number*means an arbitrary variableA first number is written as x

A second number is written as y

__Twice a second number means we multiply y by 2:__

2y

__A first number plus twice a second number:__

x + 2y

__A first number plus twice a second number is 10 means we set x + 2y equal to 10:__

x + 2y = 10

__Twice the first number means we multiply x by 2:__

2x

__Twice the first number plus the second:__

2x + y

__Twice the first number plus the second totals 35 means we set 2x + y equal to 35:__

2x + y = 35

Therefore, we have a system of two equations:

- x + 2y = 10
- 2x + y = 35

- -2x - 4y = -20
- 2x + y = 35

(-2 + 2)x + (-4 + 1)y = -20 + 35

The x terms cancel, so we have:

-3y = 15

To solve this equation for y, we type it in our search engine and we get:

y =

**-5**

Now we substitute this y = -5 into equation 2:

2x - 5 = 35

To solve this equation for x, we type it in our search engine and we get:

x =

**20**