How do you work with algebra problems like this???

Question

6x-3y=42
4x+2y=-4

what is x+y?

Answer 1

12x - 6y = 84
12x + 6y = -12
24x = 72
x = 3
y = -8 (back substitution)
x + y = -5

Answer 2

There are three ways that come to mind
substitution, elimination, and matrix methods

Lets do elimination
1) 12x-6y=84 mult first equation by 2
2) 12x+6y=-12 mult second equation by 3
3) -12y=96 subtract 2 from 1
4) y=-8
5) 6x-3(-8)=42 substitude back into first equation
6) 6x+24=42 multiply
7) 6x = 18 subtract 24 to each side
8) x = 3

9) 6(3)-3(-8) = 42 check
10) 4(3) +2(-8) = -4 check

Answer 3

what are x and y? Solve the system:

a) 6x-3y=42
b) 4x+2y=-4

by any method. try substitution:

a) 6x-3y=42 or
6x =42 + 3y, div by 6
x = 7 + .5 y. subs in b)

b) 4x+2y=-4 becomes
4(7+.5y) +2y = -4, expand
28 + 2y + 2y = -4, gather
4y = -4 -28, note signs or
4y = -32
y = -8. subs in
x = 7 + .5 y or
x = 7 + .5(-8) or
x = 7 - 4 or
x=3.

so, x + y = 3 - 8 = -5.

Answer 4

6x + 6y = 42 + 9y
x + y = 7 + 3y/2
4x + 4y = 2y - 4
x + y = y/2 - 1
(x + y - 7)/3 = x + y + 1
(x + y)/3 - 7/3 = x + y + 1
2(x + y)/3 = - 10/3
x + y = - 5

Answer 5

6x -- 3y = 42 => 2x -- y = 14
4x + 2y = -- 4 => 2x + y = -- 2
adding we get 4x = 12 => x = 3
then 2(3) + y = -- 2 => y = -- 8
x + y = 3 -- 8 = -- 5

Answer 6

6x-3y=42=>12x-6y=84 *
4x+2y=-4=>12x+6y=-12 **
by solving eq. * and **:24x=72=>x=3
6x-3y=42=>6*3-3y=42=>-3y=24=>y=-8

x+y=3-8=-5