Help with few math problems??!?

Question

...using the elimination method to solve for the equation

5x +4y = -3

-7x - 8y = -3

... also using the the elimination method to solve this.

2x + 3y= -12

7x+ 7y = -28

and also by using substituting method

6x + 7y = -29

x= -2 - 4y

Answer 1

10x + 8y = -6
-7x - 8y = -3
3x = -9
x = -3
y = 3


14x + 21y = -84
14x + 14y = -56
7y = -28
y = -4
x = 0

6x + 7y = -29
6x + 24y = -12
17y = 17
y = 1
x = -6

Answer 2

Ok, well the first one to solve by linear combination.... multiply the top equation by 2 and add them... so you're left with.....

10x + 8y = -6
-7x - 8y = -3
_______________
3x = -9
x = -3

5(-3) + 4y = -3
-15 + 4y = -3
4y = 12
y = 3

For the 2nd one multiply the top one by 7, bottom by 2 and subtract..
7 (2x + 3y = -12) = 14x + 21y = -84
2 (7x + 7y = -28) = 14x + 14y = -56
______________
7y = -28
y = -4

2x + 3(-4) = -12
2x -12 = -12
2x = 0
x = 0

Then, the last one by substitution, you just substitute the x= equation into the first one... as follows.....

6(-2 - 4y) + 7y = -29
-12 - 24y + 7y = -29
- 17 y = -17
y = 1

x = -2 - 4 (1)
x = -2 - 4
x = -6

Answer 3

First:

2(5x+4y= -3) = 10x+8y= -6

10x+8y = -6
+-7x-8y = -3

3x = -9
x = -3

Plug into first:
5(-3) + 4y = -3
-15+4y = -3
4y = 12
y =3

x= -3 , y=3

Second:

7(2x+3y= -12) = 14x + 21y = -84
-2(7x+7y= -28) = -14x -14y = 56

14x + 21y = -84
+-14x - 14y = 56

7y = -28
y=4

Plug into first:

2x+3(4)= -12
2x+12= -12
2x=0
x=0

x=0 , y= -4

Third:

Plug in the second equation for x in the first:

6(-2 - 4y) + 7y = -29
-12-24y+7y= -29
-17y = -17
y= 1

Plug that into second equation:

x= -2 -4(1)
x= -2 -4
x= -6

x= -6 , y= 1

Answer 4

1)
in elimination method by manipulating the given equation you can eliminate one variable term by adding or subtracting

5x + 4y = -3 ---------eqn(1)

-7x - 8y = -3 -----------eqn(2)

In the second eqn y coefficient is 8 and in the first it is 4. so if you multiply eqn(1) with 2 both the y coefficients will be equal. If they are of the same sign, you can subtract and if signs are opposite you can add to eliminate. y term

2*eqn(1)

10x + 8y = -6

-7x - 8y = -3

add

3x = -9

x = -9/3 = -3

substitute this value in eqn(1)

5(-3) + 4y = -3

-15 + 4y = -3

4y = 12

y = 3

2)
2x + 3y = -12 ------------eqn(1)

7x + 7y = -28 --------------eqn(2)

2nd can be simplified

divide eqn 2) by 7

x + y = -4 --------------eqn(3)

now multiply with 2

2x + 2y = -8

now subtract this from eqn(1)

y = -4

now substitute this in eqn(3)

x -4 = -4

x = 0

3)
6x + 7y = -29

x = -2 - 4y

substitute 2nd into first

6(-2-4y) + 7y = -29

-12 - 24y + 7y = -29

-17 y = -17

y = 1

substitute this in 2nd one

x= -2 - 4

x = -6

Answer 5

I will do the first one. To use the elimination method you need to get the x or y multiplier to be the same in both equations so you can add or subtract them to eliminate a variable.

In the first set of equations I would multiply 5x + 4y = -3 by 2 so that you get 10x + 8y = -6 then add this equation to the second equation to get

3x = -9 or x = -3

Then substitute x = -3 into either equation to solve for y.

Answer 6

2(5x+4y=-3)

10x+8y=-6 eq1
-7x-8y=-3 eq2

add eq 2 from eq1

3x=-9
x=-3

to find y substitute x into one of the eq(doesn't matter which one you choose)
5(-3)+4y=-3
-15+4y=-3
4y=12
y=3

do the same thing with next problem except you time 7 to the first eq and 2 to the second eq

you should get y=3 and x=10.5

6x+7y= -29
substitute x into the eq
6(-2-4y)+7y =29 etc...

Answer 7

first problem:
first equation: multiply by 2 to make:
10x + 8y = -6
-7x - 8y= -3

3x = -9
x = -3

plug x back into original equation to find y is 3






2x + 3y = -12
7x + 7y = -28

turns into

-14x - 21y = 84
14x + 14y = -56

-7y = 28
y = -4
x = 0








6x + 7y = -29
x = -2-4y

6(-2 - 4y) + 7y = -29
-12 - 24y + 7y = -29
-17y = -17
y= 1
x= -6





hope this helps

Answer 8

(5x+4y=-3)2 --> 10x+8y=-6
10x+8y=-6 -->the 8y's cancel
-7x-8y =-3
10x+(-7x)=-6+(-3)
(3x = 3) divided by 3
x=1
To find y, substitute x as 1 so, 5(1)+4y=-3
5+4y=-3 --> 4y=-8
y=-2
_______________________________________________
(2x+3y=-12)7 ---> 14x+21y=-84
(7x+7y=-28)-2--->-14x-14y=56
ADD THE EQUATIONS---> 7y=-28 ---> y=-4
TO FIND X---> 2x+3(-4)=-12 ---> 2x-12=-12 ---> 2x=0---> x=0
_______________________________________________
Substitution:
6(-2-4y)+7y=-29 ---> -12-24y+7y=-29 --->-17y=-17 --->y=1
x=-2-4(1) ---> x=-2-4 ---> x=-6