Solve the system by the addition method.?

Question

2x + 3y = 5
3x + 2y = -5

Answer 1

3(2x+3y=5)
-2(3x+2y=-5)
y=5
x=-5

Answer 2

Add the two expression together: 5x + 5y = 0
Transpose: 5x = -5y therefore: x = -y
Substitute for x in first expression: -2y + 3y = 5, or y = 5
Substitute for y in second expression: 3x + 10 = -5,
Therefore 3x = -15, or x = -5

Proof
Substituting both values in both expressions:
-10 + 15 = 5 is true
-15 + 10 = -5 is true

Answer 3

You have to get one of the variables to cancel out, then solve for the one that's left.
-3(2x+3y=5)
2(3x+2y=5)

multiply out
-6x-9y= -15
6x+4y=10

combine
-5y=-5

get y alone by dividing by -5
y=1

Plug y=1 back into the first equation
2x+3(1)=5
2x+3=5
2x=2
x=1

So, x=1 y=1

Answer 4

-3(2x + 3y = 5)
-6x - 9y = -15

2(3x + 2y = -5)
6x + 4y = -10



-6x - 9y = -15
6x + 4y = -10
__________
0x - 5y = -25
-5y = -25
y = 5

Then plug 5 in for y in either equation to solve for x.
2x + 3(5) = 5
2x = -10
x = -5

I hope this helps!

Answer 5

2x + 3y = 5 ------A
3x + 2y = -5 ------B

A x 3: 6x + 9y = 15 -----C
B x 2: 6x + 4y = -10 ----D

C - D: 5y = 25 -> y = 5

Sub y=5 into either A or B or C or D
x= -5

Answer 6

3y=5-2x
-3
y=5-3-2x
y=2-2x

3x+2(2-2X)=-5
3x+4-4x=-5
-1x+4=-5
-5 -5
-1x=-1 divine by one
x=1

Answer 7

6x + 9y = 15
-6x - 4y = 10----ADD
5y = 25
y = 5
2x + 15 = 5
2x = - 10
x = - 5
Solution: x = - 5, y = 5