Equation Questions?

Question

Ok I have two equation questions which are:

Solve the equation: 8 + 2z = 3(2-z)

Solve Simultaneous equation:
5x + 2y =4
4x - 3y = 17

Show working please!

Answer 1

8 + 2z = 3(2 - z)

8 + 2z = 6 - 3z

8 + 2z + 3z = 6 - 3x + 3z

8 + 5z = 6

8 + 5z - 9 = 6 - 8

5x = - 2

5z / 5 = - 2 / 5

x = - 2/5

- - - - - - - - - -

Elimimation by adition method

5x + 2y = 4- - - - - -Equation 1
4x - 3y = 17- - - - - Equatioh 2
- - - - - - - - -

Multiply equation 1 by3 and equation 2 by 2

5x + 2y = 4

3(5x) + 3(2y) = 3(4)

15x + 6y = 12

- - - - - - - - - - -

4x - 3y = 17

2(4x - 2(3y) = 2(17)

8x - 6y = 34

- - - - - - - - - -

Elimination of y

15x + 6y = 12
8x - 6y = 34
- - - - - - - - - - -
23x = 46

23x / 23 = 46 / 23

x = 46 / 23

x = 2

Insert the x value into equation 1

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

5x + 2y = 4

5(2) + 2y = 4

10 + 2y = 4

10 + 2y - 10 = 4 - 10

2y = - 6

2y / 2 = - 6 / 2

y = - 6 / 2

y = - 3

Insert the y value into equation 1

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

Check for equation 1

5x + 2y = 4

5(2) + 2( - 3) = 4

10 + (- 6) = 4

10 - 6 = 4

4 = 4

- - - - - - - - -

Check for equation 2

4x - 3y = 17

4(2) - 3( - 3) = 17

8 - (- 9 ) = 17

8 + 9 = 17

17 = 17

- - - - - - - -

Both equations balance

The solution set is { 2, - 3)

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

Answer 2

8 + 2z = 3(2-z)
8+2z = 6-3z
5z = -2
z = -2/5

Solve Simultaneous equation:
5x + 2y =4
4x - 3y = 17
15x+6y = 12
8x-6y=34
23x = 46
x = 2
if x = 2,
5(2)+2y=4
10+2y = 4
2y=-6
y=-3

Answer 3

8 + 2z = 3(2-z)

First multiply out the bracjets

8+ 2z = 6- 3z

Next add 3z to both sides

8+ 2z+3z= 6

8+ 5z = 6

Subtract 8 from both sides

5z= 6-8

5z= -2

z= -2/5 or -0.4.

5x + 2y =4 (eq 1)
4x - 3y = 17 (eq 2)

multiply equation 1 by 3 and equation 2 by 1

15x + 6y = 12 (eq 3)
8x - 6y = 34 (eq 4)

Add equations 3 and 4

15x+ 8x + 6y-6y = 12 +34
23x = 36
x= 36/23 = 1.5652.

Substitute this into equation 1

5*1.5652 +2y = 4
7.82609 +2y =4

2y = 4-7.82609
2y= -3.82609
y= -3.82609/2= -1.9130

Answer 4

Problem One

8 + 2z = 3(2 - z)

Expand brackets

8 + 2z = 6 - 3z

Collect terms

8 - 6 = - 3z - 2z

2 = - 5z

z = - 5/2

z = - 2.5


Problem Two

5x + 2y = 4.......................Eq 1
4x - 3y = 17.....................Eq 2

Make the coefficient of x the same in both Equations

Multiply Eq 1 x 4

20x + 8y = 16.................Eq 3

Multiply Eq 2 x 5

20x - 15y = 85.................Eq 4

Subtract Eq 4 - Eq 3
- 23y = 69

Divide and solve for y
y = - 3

Substitute y = - 3 in Eq 1
5x + {2(-3)} = 4

5x - 6 = 4

5x = 10

Divide and solve for x

x = 2

You can check back in Eq 2

4 x 2 - 3(-3) =
8 + 9 which do indeed = 17


Always REMEMBER Whatever you do to LHS of Equation you MUST DO the same to RHS of Equation

Also Remember BODMAS

Brackets

Of (Power)

Division

Multiplication

Addition

Subtraction

The sequence of Operations in ANY Formulae or Equation Calculation.

And if you require to separate /isolate groups of terms then you USE brackets

Answer 5

No, the above (simultaneous equations) is wrong.

5x + 2y = 4
4x - 3y = 17

Multiply 1st eq. by 3 and the 2nd by 2 (the coefficients of "y")
15x + 6y = 12
8x - 6y = 34

Add the 2 equations together (to remove all "y"s)
23x = 46
x = 2

Substitute value of x into either equation (e.g. the 1st)
10 + 2y = 4
2y = -6
y = -3

[To check, substitute the values found into the other (2nd) equation...
4x2 - 3.(-3) = 8 + 9 = 17 ----- check OK!]
.

Answer 6

8 + 2z = 3(2-z)
8 - 6 = z(-3-2)
-2/5 = z

5x + 2y = 4
4x - 3y = 17

>> 15x + 6y = 12
>> 8x - 6y = 34

adding gives 23x = 46 so x=2

sub into first equation 10 + 2y = 4
2y = -6
y = -3

Answer 7

Question 1
8 + 2z = 6 - 3z
5z = - 2
z = - 2/5

Question 2
15x + 6y = 12
8x - 6y = 34--------ADDING gives
23x = 46
x = 2
10 + 2y = 4
2y = - 6
y = - 3
Solution is x = 2 , y = - 3

Answer 8

Simplifying
8 + 2z = 3(2 + -1z)
8 + 2z = (2 * 3 + -1z * 3)
8 + 2z = (6 + -3z)

Solving
8 + 2z = 6 + -3z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '3z' to each side of the equation.
8 + 2z + 3z = 6 + -3z + 3z

Combine like terms: 2z + 3z = 5z
8 + 5z = 6 + -3z + 3z

Combine like terms: -3z + 3z = 0
8 + 5z = 6 + 0
8 + 5z = 6

Add '-8' to each side of the equation.
8 + -8 + 5z = 6 + -8

Combine like terms: 8 + -8 = 0
0 + 5z = 6 + -8
5z = 6 + -8

Combine like terms: 6 + -8 = -2
5z = -2

Divide each side by '5'.
z = -0.4

Simplifying
z = -0.4

Answer 9

8 + 2z = 3(2-z)
8+2z = 3-3z
5z = - 5
z=-1

[Edited - i did a mistake at the beginning, but i found without seeing others solution]
5x + 2y =4
4x - 3y = 17

2y=4-5x
x = 3y+17

y=2 -5x/2
x = 3y/4+17/4

y=2 -5x/2
x = 3/2 -15x/8 + 17/4

y=2 -5x/2
8x = 12 -15x + 34

y=2 -5x/2
23x= 46

y=2 -5
x=2

y=-3
x=2

Answer 10

triple the top and double the bottom so:
15x + 6y = 12
8x - 6y = 34
then add so"
23x = 46
x = 2

substitute it bak in :
(5 x 2) + 2y = 4
10 +2y = 4
2y = -6
y = -3

now,
8 +2z = 6 - 3z
2=-5z
z= -2/5