Solving systems of equations?

Question

My daughter is working on solving for system of equations and is asking for my help...Can anyone tell me the answers to these and explain the steps in a way I can explain to her and she will understand??? Thanks

x-y=3
2x-y= -1 and the other one is


2x+4y=10
3x-2y= -9

Answer 1

The idea is to combine the equations in such a way that one of the unknowns is eliminated, and then you solve for the remaining one.
e.g. Take the second pair (slightly harder than the first)
Notice the second equation contains -2y, so if we double everything we have -4y, which will cancel out the 4y in the first equation if we add them together:

2x + 4y = 10
6x - 4y = -18
Now use the principle that if we add together two left sides that are equal to the two right sides, the resulting sums must be equal. Adding:
8x = -8
Therefore x = -1.

I point out here that in this case, multiplying is not necessary: We could just divide each term in the first equation by 2 and get
x+2y=5
3x-2y=-9
Adding:
4x = -4

Of course, we have to find y as well, but that's easy once we know x: Just substitute the value we found in either of the two equations, it should give us the same answer for y whichever one we use.

So put x = -1 in the first equation, which then becomes
2*(-1)+4y=10

-2 + 4y = 10
4y = 12
y = 3.

I just noticed I'm wasting my time as others have already answered for you!

Answer 2

x - y = 3- - - - - -Equation 1
2x - y = 1- - - - -Equation 2
- - - - - - -
Multiply equation 1 by - 1
x - y = 3

-1(x) - (-1)(Y = -1(3)

-x + y = - 3. . . .new equation 1

- - - - - - - - -

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

The answer is x = - 4

Insert the x value into equation 1

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

x - y = 3

- 4 - y = 3

- 4 - y + 4 = 3 + 4

- y = 7

-1(- y) = -1)7)

y = - 7

The answer is y = - 7

Insert the y value into equation 1

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

Check for equation 1

x - y = 3

- 4 - (- 7) = 3

-4 + 7 = 3

3 = 3
- - - - - - - - - -

Problem 2

2x + 4y = 10- - - - - -Equation 1
3x - 2y = - 9- - - - - -Equation 2
- - - - - - - -
Multiply equation 2 by 2

3x - 2y= - 9

2(3x) - 2(2y) = - 2(9)

6x - 4y = - 18. . . New equation 2
- - - - - - - - -

2x + 4y = 10
6x - 4y = - 18
- - - - - - - - -
8x = - 8

8x/8 = - 8/8

x = - 1

The answer is x = - 1

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

2x + 4y = 10

2(- 1) + 4y = 10

- 2 + 4y = 10

- 2 + 4y + 2 = 10 + 2

4y = 12

4y/4 = 12/4

y = 12/4

y = 3

The answer is y = 3

Insert the y value into equation 1

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

Check for equation 1

2x + 4y = 10

2(-1) + 4(3) = 10

- 2 + 12 = 10

10 = 10

- - - - - - -

Check for equation 2

3x - 2y = - 9

3(- 1) - 2(3) = - 9

- 3 - 6 = - 9

- 9 = - 9

- - - - - - - - - -

The solution set is { - 1. 3 }

- - - - - - - - -s-

Answer 3

1) You want to get the y by itself.
* Remember: what you do to one side you do to the other

x- y=3 You subtract x from x and 3.
x would go away.
-x -x

2) This is what you would HAVE LEFT:

-y=3


*Remember: When a variable is a negative (y), you have to didvide both sides by -1

3) -y=3
Divide both sides by -1

4) Final answer:
y=-3

She would do the same thing for the other one. When she gets both for the system, she will put them as if she will graph them.

Example: (0,3)
( x,y)

Answer 4

5x + 2y = 15 -5x - 2y = -5 _____________ 0 = 10 you settle on utilizing combining words, you upload both equations. 0=10 ability this gadget of equation has no answer in any respect, because the slopes of both lines are an same, in different words are parallel lines, so there is not any longer aspect of interception

Answer 5

x-y=3 ---1
2x-y=-1 ----2

now subtract equation 2 from 1..when we subtract sign of equation 2 will change

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

therefore, x= -4
now substitute it in equation 1
-4-y=3
-y=3+4
-y=7
y= -7

so x=-4 and y=-7

now, 2nd one..............here co-effiecents are different in both equation, so multiply such that for aqtleast one variable co-effiecents become same.. so multipy 2nd equation with 2

so it will beocme , 6x-4y= -18

now add both equation

2x+4y=10
6x-4y=-18
-------------
8x=-8
x= -1

now, substitute it 1st equation

2(-1)+4y=10
-2+4y=10
4y=10+2
4y=12
y=3