## MightySmurf 4 years ago Solve this system of equations using the addition method? x-y=6 -3y=x+22 Solve this system of equations using the addition method? x-y=6 -3y=x+22 @Mathematics

1. VeryShy

y=-7 x=13

2. VeryShy

that true?

3. amistre64

scale the 1st by -3

4. amistre64

-3x +3y = -18 -3y = x+22 ---------------- -3x = x+4 -4x = 4

5. MightySmurf

how do you get x+4

6. amistre64

by using the "addition" method ... you add the 2 equations together after you modify one of them by a scalar

7. amistre64

a scalar just means some number that you multiply the whole equation by to scale it up or down to something that you can use

8. MightySmurf

o so i just substitute it

9. amistre64

well, substitution will work as well; but this is a new method for you to learn so that you have many ways you can attack a problem to get to a solution

10. amistre64

this "addition" method is also commonly refered to as "elimination" since the goal is to eliminate one of the variables

11. MightySmurf

o ok thank you u make it sound easier to solve

12. MightySmurf

so if i were to have -8x+3y=-5 and 8x-2y=6 i would add the _8x and the 8x to get zero then 3-2y to get y and -5+6 to get 1 right

13. amistre64

practice helps :) the steps are pretty much like this: x - y = 6 ; (1) -3y = x + 22 ; (2) given 2 equations lets multiply one of them by a "n"umber to scale it. the easiest one would be the first one to me n(x - y = 6) ; (1) -3y = x + 22 ; (2) nx - ny = 6n ; (1) -3y = x + 22 ; (2) now what does "n" have to be to get rid of the -3y? id say n = -3 will work -3x - -3y = 6(-3) ; (1) -3y = x + 22 ; (2) -3x +3y = -18 ; (1) -3y = x + 22 ; (2) now we can add the equations together: -3x +3y = -18 ; (1) -3y = x + 22 ; (2) ---------------------- -3x = x + 4 ; (3) and solve the new equation (3) for the remaining variable

14. amistre64

if they give you: -8x+3y =-5 8x-2y = 6 then yes the x parts are already set up for elimintion, just add the 2 equations together

15. MightySmurf

ok thank u sooo much i would give u thousands of medals if i could

16. amistre64

youre welcome, and good luck ;)