How many solutions does the system have? You can use the interactive graph below to find the answer.
y=x+1
y = 2x – 5
Choose 1

The answer has one solution:

       →  x = 6 ; y = 7 ;  or, write as:  [6, 7].

Step-by-step explanation:

Given:

y = x + 1;

y = 2x – 5 ;

2x  – 5 = x + 1  ;  Solve for "x" ;

Subtract "x" ; and Subtract "1" ; from Each Side of the equation:

   2x  – x  – 5  – 1 = x  – x  +  1  –  1 ;

to get:  

   x   –  6  =  0  ;

Now, add "6" to Each Side of the equation;

       to isolate "x" on one side of the equation;

        and to solve for "x" :

    x   –  6   +  6 =  0  +  6  ;

to get:

       x  =  6 .

Now, let us solve for "y" ;  

We are given:  

  y =  x + 1  ;

Substitute our solved value for "x" ; which is:  "6" ; for "x" ; into this given equation; to obtain the value for "y" :

 y =  x + 1 ;

    =  6 + 1 ;

 y =  7 .

Let us check our answers by plugging the values for "x" and "y" ;

("6" ; and "7"; respectively);  into the second given equation; to see if these values for "x" and "y" ; hold true:

  Given:  y = 2x –  5 ;

        →  7 =? 2(6) –  5 ??  ;

        →  7 =? 2(6) –  5 ??  ;        

        →  7 =?  12   –  5 ??  ;

        →  7 =?   7 ?? ;

        →  Yes!

The answer has one solution:

       →  x = 6 ; y = 7 ;  or, write as:  [6, 7].

Hope this is helpful!  Best wishes!

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents