1. consider the system of equations.
x-5y=2, 3x-10y=11

(a) jamar rewrote the first equation as –2x + 10y = –4. what justification did he have for doing this?
(b) jamar combined the equation in part (a) with the second equation in the system to get x = 7. explain jamar’s reasoning.
(c) what is the solution of the system?
(d) how do you know, without graphing, that the graph of 4x – 15y = 13 passes through the point whose coordinates are the solution of the system?

A) Jamar rewrote the first equation as -2x + 10y = -4.  He had justification for doing this because he multiplied all parts of the expressions on both sides of the equation by the same factor, -2.

B) Jamar combined -2x + 10y = -4 with the other equation, 3x-10y=11, to get x=7.  To do this, Jamar used combination, combining each of the different parts of the equations together. The y variables cancel out, and the x variables leave 1x, and we subtract 4 on the right side of the equation, leaving x = 7.  

C)The solution of the system in an ordered pair (x,y) is (7, -1).  You can get the y variable by substituting the x variable that we know equals 7, back into either of the beginning equations, to get the y value.

D) You know, without graphing, that the graph of 4x-15y=13 passes through the point whose coordinates are the solution of the system, because if we plug in the ordered pair (7,-1) into the equation it is a true statement, meaning that the variables are a solution this equation too.  Therefore, if it were to be graphed, it would go through the point (7, -1).