algebra help plz about elimination?

Question

Use elimination to solve each system of equations.

1. 6x-5y=27
3x+10y= -24

2. 11x-5y=80
9x-15y=120

3. 5x+3y=12
4x-5y=17

thank you so much = )!!!

Answer 1

1.
6x-5y=27
3x+10y= -24 double this equation
6x + 20y = - 48 subtract this from first equation
6x-5y - (6x+ 20y) = 27 - -48
-25y = 75
y = -3 then substitute for y in the second equation
3x + 10*-3 = -24
3x = -24+30 = 6
x = 2

2. 11x-5y=80 triple this equation
33x - 15y = 240
9x-15y=120 then subtract this one
24x = 120
x = 5
substitute for x in the first equation
11*5 - 5y = 80
55 - 5y = 80
-25 = 5y
-5 = y

3. 5x+3y=12 multiply this equation by 5
4x-5y=17 multiply this equation by 3

25x + 15y = 60
12x - 15y = 51 add the two
37x = 111
x = 3
substitute for x in the first equation
5*3 +3y = 12
3y = -3
y = -1

Answer 2

All are solved in the same manner. If you can do one, you can do all. I'll show you how to do the first one.
Examine the 2 equations. The y terms look promising: -5y in the 1st and +10y in the 2nd. If you multiple both sides of the first equation by 2 you will get

12x - 10y = 54; now add this to the 2nd equation
3x + 10y = -24
Note that the y term is eliminated (-10y + 10y = 0)
and 12x + 3x = 15x and 54 - 24 = 30, so the addition yields-

15x + 0 = 30
so x=2 (x = 30/15)

Since x=2, you can substitute 2 for x in the 1st or the 2nd equation to solve for y. Using the first equation-
6*2 - 5y = 27
12 - 5y = 27
-5y = 27-12
-5y = 15
y = 15/(-5) = -3

Answer 3

1. 6x-5y=27
3x+10y= -24 Multiply 2nd equation by -2 and add to 1st Eq:
-25y = 75 --> y= -3, so x =(27-5(-3))/6= 7

2. 11x-5y=80<-- Eq 1
9x-15y=120 <--Eq2
-33x +15y = -240 <--Eq 3 = -3 times Eq1
-24x = -240
x = 10, so y = (120-90)/-15 = -2

3. 5x+3y=12
4x-5y=17
25x +15y =60 <-- 1st Eq multiplied by 5
12x -15y =51 <-- 2nd Eq multiplied by3
37x = 111 --> x = 3
5(3) +3y = 12
3y = -3
y = -1

Answer 4

1.) multiply each term on the top equation by 2. This will let you eliminate the y term leaving you with 15x=30, x=2, Then substitute 2 in for x in either equation and solve for y.

2.) multiply each term on the top by -3.

3.) try multiplying the top terms by 5, and the bottom terms by 3 to create new equations. The y will will be eliminated. Solve for x and then substitute to find y.