maths help plz?

Question

solve these simutaneouse equations

1. 3 y - 8 x =24
3 y - 2 x = 9


2. y = 13 - x
3x + 2y =16

last one

3. y+1 =2x
y = x + 2


plz help show ur working so i understand

Answer 1

1) 3y-8x=24
-1*(3y-2x)= -9
2) -3y+2x= -9
add1 and 2
6x=15
x=15/6
place it back into the equastion
3y+5=9
y=14/3

follow same format for the other ones.... get variables to one side and make one of them cancel
... answers....
#2 x= -10
y= 23

#3 x=3
y=5

Answer 2

Prob 1: All you have to do is match al element in the first eq. with one in the second, and substitute:

3y = 24 + 8x and 3y = 9 + 2x

let these two equal each other (since 3y = 3y, the other sides also do)

24 + 8x = 9 + 2x

6x = -15

x = -15/6 = -2.5

Back to the original equations:

3y - 2(-2.5) = 9

3y + 5 = 9
y = 4/3

Check: 3(4/3) - 8(-2.5) = 4 + 20 = 24 All good

Prob 2. Just subs eq. 1 into eq 2.

3x + 2(13 - x) = 16

3x + 26 - 2x = 16

x = -10

Subs back: y = 13 - (-10) = 23

Check: 3(-10) + 2(23) = 16. All good.

Prob 3. Same as above.

(x + 2) + 1 = 2x

x = 3

Subs: y = 3 + 2 = 5

Check: 5 + 1 = 2(3) = 6. All good.

Enjoy

Answer 3

1) From the first equation we find:

3y = 24+8x ( y = 8 + 8/3x)

substitution to second equation gives:

3y - 2x = (24+8x) - 2x = 9;
24 + 6x = 9;
6x = 9 - 24;
6x = -15
x = -2.5;

y = 8 + 8/3x = 8+8/3*(-2.5) = 8 - 20/3 = 24/3 - 20/3 = 4/3

Answer : x = -2.5; y = 4/3

2) 1st equation says y = 13 - x. Then we can change left side of the second equation as follows:
3x + 2y = 3x + 2(13-x) = 3x + 26 -2x = x + 26;
The right side of the second equation stays the same. Putting both sides together, we get
x+26 = 16; x = 16-26; x = -10

y = 13-x = 13-(-10) = 13+10 = 23;
Answer: x = -10 y = 23

3) From 1st equation we get y = 2x-1. Substituting this to the left side of the second equation we get:
2x-1 = x+2; 2x-x = 2+1;

The right side of the second equation stays the same. Putting both sides together, we get
x+26 = 16; x = 16-26; x = -10

y= 2x-1 = 2*(-10)-1 = -20-1 = -21

Answer: x = -10; y = -21

Answer 4

1. 3y - 8x = 24
3y - 2x = 9
First, multiply the bottom equation by (-1). You could multiply the top by (-1) if you want, but I always start with the bottom.

3y - 8x = 24
-3y +2x = -9 Now you can cancel the Y's
------------------------
-8x = 24
2x = -9 Now you can add the X's and numbers
---------------------
-6x = 15 Now divide both sides by -6
x = 15/-6
x = -5/2

Now you can put x = -5/2 into one of the equations to get y.
3y - 8x = 24
3y - 8(5/2) = 24
3y - 20 = 24
3y = 4
y = 4/3

Your answer is x = -5/2 , y = 4/3


2. y = 13-x
3x +2y =16
First, subtract the 3x from the bottom equation from both sides

y = 13 - x
2y = 16 - 3x Multiply the top equation by -2
------------------------
-2y = -26 + 2x
2y = 16 - 3x now cancel out the y's
----------------------------
0 = -26 + 2x
0 = 16 - 3x now add the x's and numbers
---------------------------
0 = -10 - x add x to both sides
-----------------------
x = -10

Now you can but x = -10 into one of the equations.
y = 13 - x
y = 13 - (-10)
y = 13 + 10
y = 23

So your final answer is x = -10 and y = 23

3. y + 1 = 2x
y = x +2 First start by multiplying the bottom equation by -1
--------------------------
y + 1 = 2x
-y = -x - 2 Now you can cancel out the y's
--------------------------------
1 = 2x
0 = -x -2 Add 2 to both sides
-----------------------------
1 = 2x
2 = -x now add the x's and numbers
----------------------------
3 = x

Now you can put x = 3 into one of the equations.
y = x + 2
y = 3 + 2
y = 5

So your final answer is x = 3 and y = 5

Answer 5

The idea here is to get either the x or the y term to drop out when you add/subtract the two equations together.

First one: (this is the hardest one )subtract the 2nd equation from the first (watch how you change the signs). The "y"term drops out; solve for x
+3y - 8x = 24
-3y +2x = -9
-------------------
-6x = 15
x = -15/6

Now that you know what x is, substitute its value back into either one of the original equations (I thought using the 2nd one was easier). Solve for y.

3y-2(-15/6) = -9
y = -14/3

You now know x = -15/6 and y = -14/3 Ta da!

(You should substitute these two numbers back into one of the original equations to check to make sure they work)

2nd one

rearrange the first equation so that the x and y are on the same side of the equation. It becomes x + y = 13

Multiply this equation by 3 and then subtract it from the 2nd equation (watch how you change the signs). The x term will drop out. (You could also multiply by 2 and then subtract causing the y term to drop out).

+3x + 2y = 16
-3x - 3y = -39
------------------
-y = -23 (multiply by -1 to make the y term positive)
+y = +23

Now that you know that y is 23, substitute it back into either of the original equations and solve for x (I chose the first equation)
23 = 13-x
x = -10


You now know x = -10 and y = 23 Ta da!
(check your work)

3rd one

rearrange both equations so the x and y terms are on the same side.

2x-y = 1
x - y = -2

Then subtract the second equation from the first equation (watch how you change the signs). The y term will drop out; solve for x.
+2x-y = 1
-x +y = +2
----------------
x = 3

Now that you know what x is substitute it back into either of the original equations ( I chose the second one)

y = 3 = 2
y = 5

You now know x = 3 and y = 5 Ta da!
Check your work.

Answer 6

(1)y = 13 - x
(2)3x + 2y =16

so rearrange (2) 2y = 16 - 3x
y = (16 - 3x) / 2
put that into (1)

(16-3x)/2 = 13 - x
16 - 3x = (13 - x) * 2
16 - 3x = 26 - 2x
16 = 26 - 5x
16 + 5x = 26
5x = 10
x = 2



NOW find out what Y is
so put x back into the first equation
y = 13 - x
y = 13 - 2
y = 11

Answer 7

1.
3y - 8x = 24
3y - 2x = 9

multiply the bottom one by -1

3y - 8x = 24
-3y + 2x = -9

Now add them:

0 - 6x = 15
=> 6x = -15
=> x = -15/6

3y + 2x = 9
=> 3y + 2(-15/6) = 9
=> 3y = 9 + 2(15/6)
3y = 9 + 5 = 14
=> y = 14/3

Answer 8

1) ged rid of x
3y-8x=24
-12y-8x= -36
add them up
-9y= -12
y= 4/3

sub 4/3 for y
3(4/3)-2x=9
4-2x=9
-2x=5
x= -5/2

Answer 9

last one is.
x+2+1=2x
x+3=2x
3=2/3x
not sure