Which of these is the solution to the system of equations?
y=2x+4
y=3x+1

is the
a. (3,10)
b. (10,24)
c. (4,12)
d. (10,3)

 [A]:  " (3, 10) ". 

Explanation:

Since:  y = 2x +4 = 3x + 1 ;  Solve for "x" ;

     2x + 4  = 3x +  1  ;  

 Subtract "2x"  and subtract "4" from each side of the equation:


2x + 4 − 2x − 4 = 3x + 1 − 2x − 4 ;

 to get:      0  = x  − 3 ;

Add "3" to both sides of the equation:

                0 + 3 = x − 3 + 3 ; 

 to get:    3 = x ; 

↔  x = 3 ; 

Now, let us plug "3" into "x" for one of the equations given, to solve for "y" ; 

Start with the first equation:

  y = 2x+4 ;    y = (2*3) + 4 ;  y = 6 + 4 ;  y = 10 .

Let us try with the second equation, to check our

y = 3x +1 ;    y = (3*3) + 1 ;  y = 9 + 1 ;  y = 10 ;  Yes!  

So, x = 3, y = 10 ;  or  (3, 10) ;  which is:  Answer choice:  [A].