Solve the system by addition.?

Question

–2x + 3y = 0
x + 2y = –14

Answer 1

–2x + 3y = 0 |
x + 2y = –14 /*2 |+
------------------
x + 2y = –14
7y = -28 <=> y = -4 => x = -6

Answer 2

y= -4
x= -6

The two ways for solving those equations are substitution and addition. Solving the system by addition means to obviously add those to equations. So, if you want to solve the system x+4y=8 and -x+2y=10, then you would write it out like you are adding two numbers (Solving the system by addition means that you are trying to cancel out either of the two variables, x or y.)
-x+2y=10
x +4y=8
__________
6y=18
y = 3

If you want to solve
–2x + 3y = 0
x + 2y = –14
______________

You can't add the Xs or the Ys, so multiply through by a number that would help you, which can be 2.
So,
–2x + 3y = 0
2(x + 2y) = 2(–14)
_______________


–2x + 3y = 0
2x + 4y = –28
______________
7y= -28
y= -4

Now, to solve for x, you substitute -4 for y (into any of the two problems that you want.) So, x+2y= -14
x+2(-4)=-14
x-8=-14
x= -6

Answer 3

multiply the second equation by +2

Then add the resulting equations ---
-2x + 3y = 0
2x + 4y = -28

To get this:

0x + 7y = -28
Divide each side by 7 to isolate the y
y = -4

Substitute the value for y into either of the original equations:
x + 2 (-4) = -14
Solve for x:
X + -8 = -14
x = -6

Answer 4

–2x + 3y = 0
x + 2y = –14 | *2
--------------------------
–2x + 3y = 0
2x + 4y=-28
--------------------------/+
7y=-28

y=-28/7=-4

x + 2y = –14
x=-14-2y=-14-(-8)=-14+8=-6

x=-6
y=-4

q.e.d.

Answer 5

-2x+3y=0
x+2y=-14

x+2y=-14
x=-14 -2y

-2x+3y=0
-2(-14-2y)+3y=0
28+4y+3y=0
28+7y=0
7y=-28
y=-4

x+2y=-14
x+2(-4)=-14
x-8=-14
x=-6

so your solutions are x= -6 and y= -4

Answer 6

-2x + 3y = 0
2x + 4y = - 28----ADD
7y = - 28
y = - 4
x - 8 = - 14
x = - 6
Solution: x = - 6, y = - 4

Answer 7

-2x+3y=0
x+2y=-14

2(x+2y)=2(-14)

2x+4y=-28
-2x+3y=0
7y=-28
y=-4

x+2(-4)=-14
x+-8=-14
x=-6

(-6,-4)