Math Homework. Help please! [Solving Systems by Elimination!!]?

Question

Okay we're solving systems by elimination, and I don't get it!!!
Can you maybe step-by-step it?
The problems are:

2) x+2y =2
5x - 3y = -29


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


6) 3x-5y=61
3x-y=17


8) 5x+2y=24
4x+3y=29

FRANCIS91- Yes. I'm a ninth grader. My teacher moves way too fast for our class, and he never offers tutorials. I seem to understand it better when people explain it to me over here. So if you don't know the answer, or don't know how to help me, pelase don't even look at my question. Okay?

JUNO622- Really. Shut up. I tried for an hour and can't understand it. I didn't want people to actually DO my homework for me. I was hoping they could pick a question and step-by-step it.

Answer 1

Elimination means Eliminating the terms and solving
So here i go... Give me a sec.

EDIT:

2) x + 2y = 2
5x - 3y = -29
Well we can either eliminate x or y terms I suggest we eliminate x first it looks easier. So what do we need to do to cancel out the x's? Well we can multiply the first equation with -5 and then add it to equation two which will cancle the x's
So take x + 2y = 2 and multiply it by -5, so you have
-5x - 10y = -10
now take this and add it to equation 2
-5x - 10y = -10
+ 5x - 3y = -29
by doing this it eliminates the x terms by adding we get
0x - 13y = -39
now divide both sides by -13
y = -39/-13
y = 3 (So now we have y) now use similar method to cancel y
So how do we cancel y? Well we can multiply the 1st equation by 3 and the second equation by 2 and then add them together this will cancle the y terms and we can solve for x. So multiply the first one by 3 and we get
x + 2y = 2 multiply by 3
3x + 6y = 6
now multiply the second one by 2
5x - 3y = -29 multiply by 2
10x - 6y = -58
Now that we have these 2 new equations lets add them together to cancle the y terms
3x + 6y = 6
+10x - 6y = -58
and see that the y's cancel we get
13x + 0y = -52
divide both sides by 13
x = -52/13
x = -4

So there you go ur final answer is x = -4 and y = 3 and if you need to write it in coordinates of point form then it is (-4, 3)

Well I'm only going to do the 1st one... and if you still need more help doing the problems... im me or email me... and i can help you where u get stuck.

Answer 2

I'll help with the first one: So in problem #2, I'll step-by-step it for you. The rest you can try to figure out.

#2 You have to unknowns x and y.

x + 2y = 2
5x - 3y = -29.

Take the first equation and switch it around so it equals x:

x + 2y = 2
subtract 2y from both sides of the equal sign:

x + 2y = 2
-2y = -2y
------------------------
x = 2 - 2y (so this is what the first equation becomes)

This gives you an answer for x. It's not a number, but it's an answer you can use to put into the 2nd equation to make it only have one unknown.

The answer for x from the first equation is x = 2 - 2y

Substitute (2 -2y) in place of the x in the 2nd equation..


5 (2 - 2y) - 3y = -29 All I did was use what x is equal to from the
first equation and substitute it where x
belongs.

Then just solve this equation for the one
unknown which is y.

10 - 10y - 3y = -29
10 - 13y = -29
-13y = -29 -10

-13y = -39

y = -39/-13
y = 3

Now that you have a numerical answer for y, substitute the number answer for y into the first equation and then you will be able to find out what x is equal to:

x + 2(3) = 2
x + 6 = 2
x = 2-6
x = -4

Then to check your answers (x = -4) and (y = 3), put them into the actual equations and see if the answers check.

-4 + 2(3) = 2
-4 + 6 = 2
2 =2 The first one checks. Now put the answers into the second equation:

5(-4) -3(3) = -29
-20 -9 = -29
-29 = -29 This one checks too.

That means that the answers x = -2 and y = 3 are correct.

Answer 3

Okay the easiest thing to do...is to make one of the variables (x or y) the subject and sub that into the other equation.

So for the first one:
x +2y = 2
x = 2 - 2y (minus 2y to the other side of the equation)
Sub this (x = 2 - 2y) into the other equation
5(2 - 2y) - 3y = -29 (replace the x with the first equation as you isolated the x and this can now be subbed into this second equation)
Now expand
10 - 10y - 3y = -29
Simplify
10 - 13y = -29
-13y = -39
y = 3 now sub this into either the first or second equation to get the value of x.


For the last question, as you cannot isolate the x or y in either equation. So you need to made the coefficient of either the x or y the same in both equations by multiplying.
So for example multiply the first equation by 3 to make the 2y a 6y
3 x (5x - 2y = 24)
15x - 6y = 72
And multiple the second equation by 2 to make 3y a 6y
2 x (4x + 3y = 29)
8x + 6y = 58
Now you can elimate the y's in the two equations by lining them up and adding (the trick here is if the signs are the same i.e. +6 and +6 you minus and if the signs are different you add)
So:
15x - 6y = 72 +
8x + 6y = 58 = (you add down the lines so 15x + 8x, -6y + 6y and 72 + 58) which leaves
23x = 130
x = 5.6 sub into one of the other equations to find the value of y.

I hope this helps...and good luck.

Answer 4

Hi,

I am going to try to show you step-by-step on how to approach your answer for number 8, and hopefully, I will be a clear.

The problem is:

5x + 2y = 24
4x + 3y = 29

You have two variables, X and Y, so pick which one you would like to cancel out. In this case, I chose Y to drop.

To do that, we must find a number that 2y and 3y can be that will cancel one another out. A common factor would be 6, since 2 * 3= 6, and 3 * 2 = 6.

So your goal is to try to change the original Ys into 6y, but remember, one must be a negative and one a positive for the cancellation.

So, I will multiply the top equation by a 3, and the second equation by a -2.

3 (5x + 2y = 24)

-2 (4x + 3y = 29)

Remember, you must distribute the front number into all the terms in the parentheses.

That will give me:

15x + 6y = 72
+
(-8x - 6y = -58)

You see how the 6s on both equations are cancelled out? Because a positive 6 added with a negative 6 will give you a 0.

This will leave you with:

15x = 72
+
-8x = -58

Solve the problem.

15x adds with a -8x (negative eight) will give you a positive 7x (remember the x, k?).

Write that below them.

15x = 72
+
-8x = -58
___

7x

Now, move to the other side of the equal sign. Remember to bring down the equal sign.

15x = 72
+
-8x = -58
________

7x = 14

Now, we will try to get X by itself, and the opposite of multiplication is division. Divide both side by 7, since that will cancel the coefficient that is sticking to the X.

So...

7x/7 = X (the seven is cancelled out, leaving X alone) and 14/7=2

So, x = 2

That's it, X has been solved. To solve for Y, plug the X into one of the original equation and solve for y.

5x + 2y = 24

5 * 2 + 2y = 24
10 + 2y = 24

Take 10 away from both sides, so you can have 2y by itself on the left side of the equation. That would be

10 + 2y -10 = 24 - 10


2y = 14

Again, we are trying to get Y by itself, so we need to cancel out the 2. To do that, we will do the opposite of multiplication, which is division.

2y/2 = 14/2

y = 7

So, to check, plug in both the X and Y values into the two original equations and see does it check out.

5(2) + 2(7) = 24
10 + 14 = 24
24 = 24

That checked out.

4(2) + 3(7) = 29
8 + 21 = 29
29 = 29

So is this one. So, X = 2 and Y = 7

(2,7) That's it--elimination.

Am I being a little helpful at all? =X

EDIT:

I also forgot to mention to you that not all cases require you to multiply [both] of the equation to cancel a variable out. Let's use example number 2.

x + 2y = 2
5x - 3y = -29

We will try to get rid of the X this time. To do that, notice that we only need to multiply the top equation by a [negative 5], because the bottom five is already a positive.

-5 (x + 2y = 2)

Remember to distribute the -5 to all the terms in that parenthese.

-5x -10y = -10

Now, line the equations up!

-5x - 10y = -10
+
5x - 3y = -29

So the Xs are cancelled out, which will leave you with the following:

-10y = -10
+
-3y = -29
________

A [negative 10] adds with a [negative 3] equals a -13. [Negative 10] adds with a [negative 29] will equal a -39.

So, we will then have:

-13y = -39

Divide both side by -13 to get Y by itself.

-13y/-13 = -39/-13

Y = 3

Now, follow the same procedure that I showed above: to solve for X, plug the Y into one of the original equation.

x + 2(3) = 2
x + 6 = 2

Get x alone, so you would need to subtract six from both sides.

x + 6 - 6 = 2 - 6

x = - 4

So now we have

x = -4
y = 3

Plug it into both original equations to check:

-4 + 2*3 = 2
-4 + 6 = 2
2 = 2 Yep, this works.

(5 * -4) - (3 * 3) = -29
-20 - 9 = -29
-29 = -29 This works, too.

So, not every problem requires you to multiply both of the given equations. Sometime, you can multiply one of the equation to cancel out the variable you chose.

Good luck.

Answer 5

2)
x+2y=2
5x+10y=10 ---(1)

5x-3y=-29 ---(2)

minus (2) from (1):
13y=39
y=39/13
y=3

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

Done...thats one question....if beg me hard enough...i will do all of them....MUAHAHA

4)
x-2y=-3
2x-4y=-6 ---(1)

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

because (1) contradicts with (2): no solution.

i pity u...who gave u the questions....quick beg me...i'm waiting...

6)
3x-5y=61 ---(1)
3x-y=17 ---(2)

minus (2) from (1):
-4y=44
y=-11

x=(17+y)/3
x=2

8)
5x+2y=24
15x+6y=72 ---(1)

4x+3y=29
8x+6y=58 ---(2)

minus (2) from (1):
7x=14
x=2

y=(29-4x)/3
y=7

DONE!!!! Nay...forget about the begging...i just being corny....hahah....but u should really try more questions on your own...ur teacher isn't evil (^_^)....my is: gave me 3 chapters to do when i failed my test;that's nearly 1000 questions....haha...you shld worry though...i'm ninth grade and i'm learning stuff way crappy....u havn seen solving 4 simu equations using matrix method....

Answer 6

ok trick is to get one of the variables x or y the same for both equations.
x+2y=2
5x-3y=-29

make it into 5x so multiply first equation by 5

5x+10y=10
then subract the 2nd equation
5x-3y=-29
-13y=-39
devide by -13
y=3 now you can plug in 3 to solve for x

Answer 7

6) 3x-5y=61
3x-y=17

solve one

(i'm taking an extra step here, because i dont' want to deal with a negative)

3x=17+y

3x-17=y

so, y=3x-17 - plug that into the other equation

3x-5(3x-17)=61

3x-15x+85=61

combine like terms

-12x=-24

x=2 (plug this back into the equation)

3(2)-5y=61
-5y=55
y=-11

y=-11; y=2

let us know if you need additional help.

Answer 8

just get rid of x or y by multiplying it to make it the same with the second equation

Answer 9

Oh kid...this is way too easy for me. You are an eight grader or a ninth grader? If you are a ninth grader then you suck. :( Better use your own brain to solve it. How will you learn if you don't do that? Bad student.

Answer 10

baby i wish i could help you but the only ones i know are substitution combination and graphing sorry, only in 8th