```Question 27808
I need help using the substitution method so can you help me solve this problem:
3x+5y=-3
-3x+y=-15
I also need help using the combination method so maybe with these too:
1) 4x+5y=-2
5x=5-10y
2) 3y=16-2x
5x+2y=14

Last question is on graphing inequalities, i think:
4x+3y (is less than or equal to) 13
-3x+4y(is greater than or equal to) 9

1)Substitution method:
3x+5y=-3 ----(1)
-3x+y=-15 ----(2)
From (2), we have y = 3x-15 ----(*)
(adding 3x to both the sides or transferring -3x from LHS to RHS, change side then change sign)
Substituting for y in (1),
3x + 5(3x-15) = -3
3x +5X3x - 5X15 = -3
3x+15x -75 =-3
18x = -3+75
18x = 72
x = 72/18 = (18X4)/18 = 4
Putting x= 4 in (*),
y = 3x - 15
= 3X4 - 15 = 12-15 = -3
Answer: x=4 and y = -3
Verification: We have used (2) for our finding the variables.So we use (1)for verification.
Putting x=4 and y = -3 in (1)
3x+5y=-3 ----(1)
LHS = 3X4 +5X(-3) = 12-15 = -3 =RHS
Therefore our  values are correct.

I also need help using the combination method so maybe with these too:
1) 4x+5y=-2
5x=5-10y
2) 3y=16-2x
5x+2y=14

Combination method:
1) 4x+5y=-2
5x=5-10y
First of all see to it that both  the equations are in the  form Ax+By = C
The given equations are
4x+5y=-2  ----(1)X 2
5x+10y= 5 ----(2) (bringing -10y from the  right  side to the left side)
Observe that 5 and 10 are the coefficients of y respectively in the equations.
And  their lcm is 10.
Why take the lcm? It is for equalising  the coefficients of the variable  we want to eliminate.
Since  5X2 = 10, multiply equation (1) through out  by 2
8x+10y=-4  ----(3)
5x+10y= 5  ----(2)
(3) - (2)gives
(8x-5x) + 0 = (-4-5) (you may do vertical subtraction and  get  the answer faster)
3x = -9
x = -9/3 = -3
Putting x= -3 in (1),
4x+5y=-2  ----(1)
4X(-3) + 5y = -2
-12+5y = -2
5y = +12-2
5y = 10
y = 10/5 = 2
Answer: x = -3 and y = 2
Verification:Putting x = -3 and y = 2 in (2)
5x+10y= 5  ----(2)
LHS = 5x+10y
= 5X(-3)+10X2
=-15+20
=+5 =RHS  which is correct

2) 3y=16-2x
5x+2y=14
The given  equation are
2x+3y = 16 ----(1)X 2
5x+2y = 14 ----(2)X 3
(lcm of the coefficients of y is 6)
4x + 6y = 32 ----(3)
15x + 6y = 42 ----(4)
(3) - (4)implies
(4x-15x)+ (6y - 6y) = 32 - 42
-11x +0 = -10
-11x = -10
x = (-10)(-11) = 10/11
x=10/11 in (1)gives
2X(10/11) + 3y = 16
20/11 + 3y = 16
3y = 16-20/11
3y = (16X11-20)/11
3y = (176-20)/11
3y = 156/11
y = (3X52)/(3X11)
y = 52/11
Answer: x =10/11 and y = 52/11
Verification: Putting x =10/11 and y = 52/11 in  5x+2y = 14 ----(2)
LHS = 5x+2y
=5x(10/11) + 2X(52/11)
= 50/11 +104/11 =(50+104)/11 = 154/11 = (11X14)/11 = 14 =RHS which is correct