Algebra 1 system of equations y = -9x + 1 y = -4x - 4

The answer to this system of equations is:  " x = 1 " ;  y = - 8" ; 

                                                   or; write as:  " [1, - 8] " .

Explanation:

Given the system of equations:


y = -9x + 1   ; 

y = -4x − 4 ;

Solve for "x" ; and "y" ; 

 
→   y = y ; ↔

→  - 4x − 4   =   - 9x + 1  ;

Add  "4x" to each side of the equation; & add "4" to each side of the equation:


→  -4x − 4 + 4x + 4  =  -9x + 1 + 4x + 4  ; 

to get:

→   0  =  -5x + 5 ; 

↔  -5x + 5 = 0  ;

Subtract "5" from each side of the equation:

→  -5x + 5 − 5 = 0 − 5 ; 

to get: 

→  -5x = -5 ; 

Divide each side of the equation by "-5" ;
      to isolate "x" on one side of the equation; & to solve for "x" ;

→  -5x /-5 = -5 / -5 ; 

to get:

 →   x = 1  ;

Now, plug in "1 " for "x" ; in  either of the 2 (two) equations given;
           to solve for "y" ;

Let us try the first equation given:


    →    " y = - 9x + 1 " ;

     →   " y = - 9(1) + 1 ;

                  =  - 9 + 1  = - 8 . 

     →   y =  - 8 .

To check our

Now, let us try substituting " 1 " for "x" ; in the second equation;
        to see if we get the same value for "y";  that is; " y = - 8 "  ; 

     →  "  y =  - 4x − 4 "  ; 

              y =   - 4(1) + 4 ;

              y =  -  4 − 4 = - 8 .

       →  y = - 8 .

The answer to this system of equations is:  " x = 1 " ;  y = - 8 " ; 

                                                   or; write as:  " [1, - 8] "  .