Hello, I need some help. Please.?

Question

I would like to have help on this, I am homeschooled so I am not so sure on it could I please have someone help me through these problems? Id apreciate it very much.

1) 3x + y = 9
-2x + y = 4

1) x + 3y = 9
4x - 2y = -6

I sort of understand it but then again. So please help?

Answer 1

Put both equations in terms of y, by rearranging them:
y = 9 - 3x
y = 4 + 2x

Therefore, 9 - 3x = 4 + 2x
Subtract 4 from both sides:
5 - 3x = 2x
Rearrange:
5 = 2x + 3x
Simplify:
5 = 5x
Therefore, x = 1.

If you know x, substitute it in to either equation to solve for y

Second one:
x + 3y = 9,
x = 9 - 3y

4x - 2y = -6,
4x = -6 + 2y,
x = -6/4 + 2y/4

So, 9 - 3y = -6/4 + 2y/4
Rearrange,
9 + 6/4 = 3y + 2y/4
Simplify:
10.5 = 3.5y
So, y = 10.5/3.5 = 3

Answer 2

The easiest way to explain it is that if you are given 2 equations, then x and y must be equal to some exact number, but you need to find it. In the first example, define y in terms of x, so subtract the x component (3x) from both sides, getting y by itself. You get y = -3x + 9. You really haven't changed the relationship between x and y. Then plug this relationship into the second equation and solve for x.
-2x + y = 4 becomes:
-2x + (-3x + 9) = 4 because we defined that y was equal to -3x + 9
-2x - 3x + 9 = 4 OR -5x + 9 = 4 simplifies to
-5x = -5, divide both sides by -5 and get x = 1.

Substitute 1 for x in the first equation (3x + y = 9) and you get:
3(1) + y = 9 or y= 6. So x = 1 and y = 6. But dont forget to check your answer by plugging in the value for x and y into the 2nd equation:
-2(1) + 6 = 4 or 6-2 =4 4 = 4 so you are golden. Good luck, you do example 2 now to practice

Answer 3

What you need to do is multiply boths dies of one or both equations until the coefficients (the multipliers in front of the variables) are equal and opposite. Then you add the equations together to cancel one out. so in the first one, multiply BOTH SIDES of the second equation by -1.

-1(-2x + y) = -1(4)
2x - y = -4

Add that to the first eqn:

3x + y = 9
2x - y = -4
--------------
3x + 2x + y - y = 9 - 4


Combine like terms (terms that have the same variable), and you notice the y and the -y cancel eachother out (y - y = 0)

5x = 5

Divide both sides by 5, and you see that x = 1. Now you can plug this into either of the equations, and you'll be able to solve for y.

3(1) + y = 9
3 + y = 9

Subtract 3 from both sides
y = 6

So x = 1, and y = 6. We can double check by pluggin those values into the second equation, just to be sure.

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

So we know we did it right!

We can do the same with the next set. Remember to combine like terms, to always do the SAME THINGS to BOTH SIDES, and you're good. Let's multiply both sides of the first by -4:

-4(x + 3y) = -4(9)
-4x - 12y = -36

Add to the first eqn:

-4x -12y = 36
4x - 2y = -6
------------------
4x - 4x - 12y - 2y = 36 - 6

Combine like terms (x cancels out):

-14y = -42 (remember that -36 - 6 is a more negative number)

Divide both sides by -14:
y = 3

Plug into first eqn:

x + 3(3) = 9
x + 9 = 9

Subtract 9 from both sides

x = 0

Plug x = 3, y = 0 into second eqn to check:

4*0 - 2(3) = -6
-6 = -6

So you're good. Good luck.

Answer 4

Let's look at the first problem:

Both these equations are true, so if you add them together you will still get something that is true. Also, if you subtract one equation from the other, the result will still be true:

3x + y = 9
-2x + y = 4
--------------
3x - (-2x) + (y-y) = 5

3 - (-2) is 5, and the two y's disappear so:

5x = 5

This means that x = 1.

Putting a value of 1 into the first equation instead of x, we get:

3(1) + y = 9 or
3 + y = 9

So y = 6.

The second problem is slightly harder. You can't just subtract the second equation from the first. But if you multiply the first equation by 2 and the second one by 3, you'll be able to add them and the y's will cancel out, leaving you a simple equation for x.

Answer 5

3x + y = 9- - - - - - -Equation 1
- 2x + y = 4- - - - - -Equation 2
- - - - - - - - -
Substitute Method equation1

3x + y = 9

3x + y - 3x = - 3x + 9

y = - 3x + 9

Insert the y value into equation 2

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

- 2x + y = 4

- 2x + ( - 3x + 9) = 4

- 2x - 3x + 9 = 4

- 5x + 9 = 4

- 5x + 9 - 9 = 4 - 9

- 5x = - 5

- 5x / - 5 = - 5 / - 5

x = - 5/- 5

x = 1

Insert the x value into equation 1

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

3x + y = 9

3(1) + y = 9

3 + y = 9

3 + y - 3 = 9 - 3

y = 6

Insert the x value into equation 1

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

Check for equation 1

3x + y = 9

3(1) + 6 = 9

3 + 6 = 9

9 = 9

- - - - - - - -

Check for equation 2

- 2x + y = 4

- 2(1) + 6 = 4

- 2 + 6 = 4

4 = 4

- - - - - - - -

The solution set is { 1, 6 }

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

Answer 6

these are called simultaneous equations. To solve them, just make one in the form of ONE variable and put it in the second. See the solution for example

1) 3x + y = 9
-2x + y = 4

Solution

3x+y=9
bring 3x to right hand side (which changes its sign to -ve)
y=9-3x name this equation as (i)

Put this value of y in out second equation -2x+y=4
-2x+(9-3x)=4
-2x+9-3x=4
-5x=4-9
-5x=-5
x=(-5/-5)
x=1

put x=1 in equation (i)
y=9-3x
y=9-3(1)
y=6

so answer is
(1,6) or x=1 and y=6


2)x+3y=9
4x-2y=-6

solution
x+3y=9
x=9-3y ----------------(i)

put this in second equation
4x-2y=6
4(9-3y)-2y=-6
36-12y-2y=-6
-14y+36=-6
-14y=-6-36
y=(-42/-14)
y=3

put this value in (i)
x=9-3y
x=9-3(3)
x=9-9
x=0

answer is x=0 and y=3
or
(0,3)

Answer 7

First thing to do is to eleminate one variable for example y if you want to add the 2 functions, the sum of y become 2y This is y is not eliminated. So the one you do is you substract the 2 functions become 5x=5 therefore x=1, when you substitute it one of the function, y=6

Answer 8

1) x=1
y=6

2)x=0 y=3

Answer 9

3X+Y=9
-2X+Y=4
(2x -y = -4)
--------------
5x=5
x=1

3+y=9
y=9-3
y=6

Answer 10

Glad I hit on this. I haven't had to use this stuff for a long time.
Some of it is beginning to filter back in. Thanks for the question and for those who explained it so well.