Solve the system by addition.?

Question

5x + 9y = –12
x – 2y = –10

Answer 1

ok, if you want to solve it by addition, the first thing u have to do is to multiply the bottom equation by -5. then add

5x + 9y = –12
-5x + 10y = 50
-------------------------
0x + 19y = 38
y = 38/19 = 2.

then put this value back into any of the equations.
5x + 9y = -12
5x + 9(2) = -12
5x + 18 = -12
5x = -30
x = -6

Hope that helped

Answer 2

5x + 9y = -12.....(1)
x - 2y = -10.....(2)

Multiply both sides of (2) by 5

5(x - 2y) = 5(-10)
5x - 10y = -50
10y - 5x = 50.....(3)

Add (3) and (1)

5x - 5x + 9y + 10y = 50 - 12
19y = 38
y = 2.....(4)

Substitute (4) in any equation. I choose (2)
x - 2y = -10
x - 4 = -10
x = -6

x = -6, y = 2 is the solution

Answer 3

y=2
x= -6

The way that you get those answers are as follows:

Multiply the second equation by -5.
You should get: -5x+10y=50.
Then you take that equation and add it to the first equation.
You should have:
5x+9y= -12
-5x+10y=50
The 5x and the -5x cancels each other out.
9y+10y= 19y
-12+50=38
so therefore you have
19y=38
divide both sides by 19 and you have
y=2.
Then you plug 2 in for y in the first equation and you get:
5x+9(2)= -12
5x+18= -12 subtract 18 from both sides.
5x= -30 divide by 5 on both sides.
x= -6

Answer 4

multiply the second equation by -5.
5x +9y = -12
-5x +10y = 50

then add all the terms

19y = 38

divide by 19 on both sides

y = 2

plug 2 in for y in either equation (i use the second equation since it's easier)

x -2(2) = -10
x - 4 = -10

add 4 to both sides

x = -6

Answer 5

First, multiply 2nd equation by -5 to get

-5x +10y = 50

Add this to 1st equation:

19y = 38

y=2

Since x-2y= -10, then x -4 = -10, so...

x = -6

Answer 6

Multiply each term in one of the equations
by a factor, such that, when the two equations
are added together, one variable drops out.
For example, -5 for the second equation.