Please Help Find x and y in the following simultanious equations.?

Question

I need help with these equations i got from my teacher please.

Question #1
3x+2y=12
2x+y=7

Question #2
5x-y=17
2x+3y=0

Question#3
x+3y=11
2x+5y=19

#4
5x+3y=24
x+5y=-4

#5
6x-4==4
3x-2y=1

Answer 1

You need to learn how to do this. It's both simple and important.

Question #1
3x+2y=12
2x+y=7

Pick one equation, and isolate one variable:
2x+y=7
y=7-2x

Now put that value for y in the other equation:
3x+2y=12
3x+2(7-2x)=12

Then rearrange to solve for x:
3x+14-4x=12
14-x=12
-x=12-14
-x=-2
x=2

Then use one of the equations to solve for y:
y=7-2x
y=7-2(2)
y=7-4
y=3

Do the same for the others.

Answer 2

Timmy's right. He showed you solving systems of equasions by the "substitution" method (I believe that's what it's called). It works for those equations. There may be times when you can use the "addition/subtraction" method. It works like this:
Question#3
x+3y=11
2x+5y=19

We need the same number of Xs or Ys in both equasions, so I'll mutiply the top equasion by 2
2x + 6y = 22

Now, you can "subtract" the bottom equasion from the top, remembering to change signs:
2x + 6y = 22
-2x-5y=-19
And when you subtract each variable, you get
0x + y=3
so Y = 3.
Then plug that in to the first equasion
x + 3(3) = 11
x+9 = 11
x=2.

(You can check this by doing the substitution method:
x = -3y + 11
2(-3y+11)+5y=19
-6y +22 +5y = 19
-y +22 = 19
-y = -3
y = 3
x + 3(3) = 11
x + 9 = 11
x = 2)

Viola! So in this equasion, it took a couple fewer steps to use the subtraction method.

Answer 3

#1 3x=12-2y
x =4-2y\3

Therefore 2(4-2y/3)+y=7
8-4y/3+y=7
1=y/3

y=3, x=2


The basic principle is rearrange the first equation to make x the subject, substitute this expression of x into the second equation and rearrange to solve for y. Use the numerical value of y in the first equation to find the value of x.

Good luck! With practice you'll get slicker at it and see the easiest things to make the subject and which equation to use for what.

Answer 4

I understand that it is some sort of math homework given by your teacher that you are supposed to do on your own. So I am not going to do all of them. I will do the first one, you can learn from that and do the rest because all the other problems are following the same procedure.

3x + 2y =12 ----- equation one
2x + y = 7 ----- equation two

4x + 2y =14 ----- equation two x 2 (making y cancel out by subtracting eq one from two)
3x + 2y =12 ----- equation one
------------------------------------------------
x = 2
-------------------------------------------------

substituting x=2 in equation two, you get
4 + y = 7
y = 7-4
y=3

There you go, x=2, y=3

Hope you got that, now try doing the rest without other people help. You will never learn in your life unless you do it on your own.

Answer 5

y = x² - 3x + 2 and y = 3x - 7 Substituting the 2d expression into the 1st... 3x - 7 = x² - 3x + 2 Simplifying... x² - 6x + 9 = 0 ( x - 3 ) ( x - 3 ) = 0 x = 3 Then y = 2

Answer 6

Edit: I'll give you Q2 as this does indeed look like homework.

Q2
i) 5x-y=17
ii) 2x+3y=0

from i)
y=5x-17

subst into ii)
17x-51=0

so x=3

Subst into i)
y=-2

Answer 7

Is this your home work? x=2, y=3 for the first one....