Solve by addittion method?

Question

-3X+Y=3
2X-3Y=5

Answer 1

Choose either to make the x's or the y's cancel.

I choose the y's so I only have to change one equation.

-3X + Y = 3
2X - 3Y = 5

Multiply the first equation by 3:

-9X + 3Y = 9
2X - 3Y = 5

Add the two equations, so the y's drop out:

-9X + 2X + 3Y - 3Y = 9 + 5
-7X = 14
X = -2

Then plug that in either of the equations to find y:

-3(-2) + Y = 3

6 + Y = 3

Y = 3 - 6 = -3

So X = -2 and Y = -3.

Check:

-3(-2) + -3 = 3
6 - 3 = 3 check!

2(-2) - 3(-3) = 5
-4 + 9 = 5 check!

Answer 2

First method:

1) -3x+y=3
2) 2x-3y=5

1)y=3+3x

2) 2x-3(3+3x)=5 => -7x=14 => x=-2

1) y=3+3(-2) => y=-3

Second method:

1) -3x+y=3 multiply by (-2)
2) 2x-3y=5 multiply by 3


1) 6x-2y=-6
minus
2) 6x-9y=15
-------------------
7y=-21 => y=-3

1) -3x+(-3)=3 => x=-2

Answer 3

Add. the both:
-3x+y=3
2x-3y=5
________
-x-2y=8
transp. -2y to the other side.
-x=2y+8 or x=-2y-8
Replace x in any equation to find y:
-3(-2y-8)+y=3 or 6y+24+y=3
7y=-21 or y=-3
Replace y to find x:
2x-3(-3)=5 or 2x=5-9
2x=-4 or x=-2
S={-2,-3}

Answer 4

im assuming ur trying to fing Y so

-3X + Y = 3 first u add 3X to both sides
+3X +3X -3X & +3X cancel each other
Y=3X+3 so ur left wit this

2X - 3Y = 5 1st subtract -2X from both sides
-2X -2X 2X & -2X cancel each other
-3Y=-2X+5 now divided -3 to both sides
-3 -3
y= -2x+5/-3 so u would get

Answer 5

-3x+y=3>add 3x to both sides
y=3x+3

2x-3y=5>subtract 2x from each side
-3y=-2x+5>divide both sides by -3
y=-2/3x+5/3

Answer 6

-3X+Y=3 |*3
2X-3Y=5 |

-9x +3y =9 | add them
2x -3y =5

-7x =14, hence x=-2

Answer 7

-6x + 2y = 6
6x - 9y = 15

-7y=21
y= -3
plug it back into either of the original equations

2x - (-9) = 5
2x + 9 = 5
2x = -4
x = -2

now check it by going to the first equation
-3(-2) + (-3) = 3
6 - 3= 3
VOILA!