help! in the equations 2x-3y=-4 and 4x+2y=8 what system is involved... and what is the solution needed?

Question

i have this algebra class with this monotonous and boring teacher and i cant seem to understand his lectures, and we dont even have a reference book... weve just tackled consistent and independent, consistent but dependent, and inconsistent equations... this one i need help with...

Answer 1

Elimination by addition Method

2x - 3y = - 4- - - - - - - Equation 1
4x + 2y = 8- - - - - - - Equation 2
- - - - - - - - - -
Multiply equation 1 by - 2

2x - 3y = - 4

- 2(2x) - (- 2)(3y) = - (- 2)(4)

- 4x - (- 6y) = - (- 8)

- 4x + 6y = 8
- - - - - - - - - - - - -

Elimination of x

- 4x + 6y = 8
4x + 2y = 8
- - - - - - - - - - - -

8y = 16

8y / 8 = 16 / 8

y = 16 / 8

y = 2

Insert the y value into equation 1

- - - - - - - - - - - - - --

2x - 3y = - 4

2x - 3(2) = - 4

2x - 6 = - 4

2x - 6 + 6 = - 4 + 6

2x = 2

2x / 2 = 2 / 2

x = 2/2

x = 1

Insert the x value into equation 1
- - - - - - - - - - -

Check for equation 1

2x - 3y = - 4

2(1) - 3(2) = - 4

2 - 6 = - 4

- 4 = - 4
- - - - - - - - - -

Check for equation 2

4x + 2y = 8

4(1) + 2(2) = 9

4 + 4 = 8

8 = 8
- - - - - - - - - - -

Both equations balance

The solution set { 1, 2 }

- - - - - - - - - - - -s-

Answer 2

So do you mean you want to solve these equations using simultaneous equations?

If so, you can use either elimination or substitution to solve simultaneous equations.
With elimination you eliminate one pronumeral (in your case either x or y) by either adding or substracting one equation from the other inorder to be left with an equation in terms of only one pronumeral so that you are able solve what the pronumeral is equal to and then you can sub this value back into either equation to find what the other pronumeral is equal to.
With substitution, you substitute one eqn into the 2nd eqn. For eq. sub y = x into y + 2x = 4 (ie. replace the y in the 2nd eqn with x, as y = x) To use substitution you need the equation your going to sub into the other eqn to be in terms of 1 pronumeral. for eg in terms of y, which means the equation will be y = ....

So, to solve 2x - 3y = -4 and 4x + 2y = 8 simultaneously the easiest thing in your case is to get either x's or the y's to equal the same thing (so we either want both eqns to have 4x or both to have 6y)

2x - 3y = -4 ...(1)
4x + 2y = 8 ...(2)

(1) x 2: [ 2x - 3y = -4 ] x2
4x - 6y = -8 ....(3)

equation 3 - equation 2: This will eliminate the x pronumeral so the equation will be all in terms of y. We can then work out what y is equal to.
(3) -- (2): 4x - 6y - 4x - 2y = -8 - 8
-8y = -16
y = 2
Substitute y = 2 into either eqn to find what x is equal to.
sub y = 2 into eqn 1, 2x - 3y = -4:
2x - 3(2) = -4
2x - 6 = -4
2x = 2
x = 1

To CHECK if these values we worked out are correct sub both values we found for x and y back into the SAME equation and see if the equal the expected answer. For eg. if these values are correct, substituting them back into eqn 1 they should equal -4.

CHECK: Sub x = 1 and y = 2 into equation 1.
2x - 3y = -4
2(1) - 3(2) = -4
2 - 6 = -4
-4 = -4
Therefore we can conclude that these values are CORRECT as the Left hand side (LHS) = Right hand side (RHS)

Therefore x = 1 and y = 2

Hope this helps =]
Good luck!

Answer 3

These are simultaneous equations.
- 4x + 6y = 8 (after x by - 2)
4x + 2y = 8----ADD
8y = 16
y = 2
2x - 6 = - 4
2x = 2
x = 1
Solution is x = 1, y = 2

Answer 4

isolate one of the variables:

4x + 2y = 8
2y = 8 - 4x
y = 4 - 2x

substitute this in the other equation:

2x - 3y = -4
2x - [3(4-2x)] = -4
2x - [12 - 6x] = -4
2x - 12 + 6x = -4
8x - 12 = -4
8x = 12 - 4
8x = 8
x = 1

To get y:
y = 4 - 2x
y = 4 - 2(1)
y = 4 - 2
y = 2

Answer 5

This is linear equation with 2 variables x and y

2x-3y=-4
4x-6y= -8

4x+2y=8

solving both
4x-6y= -8
4x+2y=8
subtracting we get
-8y= -16
y =2

so x =1

Answer 6

2x-3y=-4.................(1)
4x+2y=8.........(2)
2*(1 gives 4x-6y=-8..........................(3
(2-(3) gives8y=16,y=2
put it in *(1),2x+6=-4,x=-5