Anyone understand Algebra in order to help me??

Question

I need help!! I don't understand how to do this!! I don't want you to just give me the answer! Please try to explain how to do the steps! I just don't get how to do this kind of problem:

4x + 4y = 8
x + 5y = 10

I need to find the value of x and y. Can you help?

Answer 1

This is called a linear equation in two unknowns. I could give you the answer but here is how to do the math (algebra). First, either add, or subtract, one equation from the other. It looks, by inspection, that by subtracting the 1st equation from the 2nd one, you will get a simpler result
eq2) x + 5y = 10
eq1) 4x+ 4y = 8
If you subtract eq1 from eq2 (remember when you subtract, you change the sign and add?) the result is -3x + y = 2 (work it out). Now, isolate the simple unknown by algebraic manipulation. Add the complex unknown to both sides of the equation. (becomes y = 2 + 3x ) Because you now know what y equals in terms of x, substitute y into equation 2 to replace the y there and everything is now in terms of x.
x + 5(2 + 3x) = 10 now solve for x. You can do it., I know you can. Having done that you now have values for both x and y. The rest is child's play. By the way, this whole thing could have been simplified by noticing that eq1 can be solved for X in the first place. My goal here is to teach you the generalized method, to apply to all such problems, not just special cases like this one.
Pay more attention in class, don't be afraid to ask questions, and try and find a study buddy. If you have a buddy, and you can't figure out a problem with him, then there are probably a lot of other kids in the class in the same boat, so by asking, you won't look like the dummy. The rest of the kids will look up to you for making them not have to ask.

Answer 2

you have to make like terms of either the x's or the y's, then add or subtract the whole equations 1 step at a time. First, we'll make both equations have a '4x' by changing the second one:
4(x+5y=10) = 4x+20y=40. Now eliminate the x's by subtracting the first equation from the second equation.
4x+20y=40 - (4x+4y=8) = 4x+20y=40
+-4x -4y =-8
= 0 +16y=32, 16y=32, y=2, following so far? now you have to substitute 'y=2' into one of your equations to come up with 'x'. 4x + 4(2)=8, 4x+8=8, 4x=0, x=0. and it's always good to try it with the other equation to make sure your right: x+5(2)=10, x+10=10, x=0.

Hope I answered your question. Soon they'll be asking you to do this with three or four equations; same premise, just takes longer. Just remember to be very careful with positives and negatives, that's where I always find my mistakes.

Answer 3

This is a system of two equations in two unknowns - two straight lines that intersect at a point. The solution is the coordinate pair of that point.

1) 4x + 4y = 8
2) x + 5y = 10

There are several ways to solve this system. In this case, I would first divide both sides of equation 1 by 4

1a) x + y = 2

Now subtract equation 1a from equation 2

x + 5y - (x + y) = 10 - 2
x + 5y - x - y = 8
4y = 8
y = 2

Plug this result into equation 2

x + 5(2) = 10
x + 10 = 10
x = 0

Lines intersect at (0, 2)

Check using equation 1

4(0) + 4(2) = 8
0 + 8 = 8
8 = 8

Sometimes you first need to multiply one of the equations by a constant to get the coefficients of one variable the same so you can then subtract.

This could be easily done bu substitution - solve equation 1a for x

x = 2 - y

Substitute into equation 2

2 - y + 5y = 10
2 + 4y = 10
4y = 8
y = 2

Answer 4

Hey over here! lol

Ok, now dont freak out! This isnt as bad as it looks. Trust me...

I'll go over it with you as I solve it so you can try it yourself on other equations. This is basically a system of equations. You can use the addition method to solve it. Most people tend to stick to it because it is the first method they learn. Plus it's a little simpler.

So you have 4x+3y=8
x+5y=10
____________

First thing you need to do is pick which variable you want to solve for. Let's use y. In order to do that, you need to cancel out the x. Always remember that you only need 1 variable (letter) in an equation like this to solve for the other. With me so far?

First cancel out, then add.

To cancel out the x's you multiply the top by -1 and the bottom by 4. The neg. 1 comes from the -x. There's an invisible one there anytime a variable is by itself. Sooo

It should look like this: -1(4x+3y=8)
4(x+y=10)
____________
Solve now. Multiply everything and carefully watch your signs. This a mistake alot of people make including myself. Anyway, your new equations should be like this.

-4x-3y= -8
+4x+4y=10
_________

Now do you see how the 4x's cancel out when you add them?
-4+4=0

Your left with -3y=8
+4y=10

-3y+4y= +y
-8+10=+2

So y=2 Dunzooo

Now just plug what y equals into whichever equation you like and solve for x. I always look for the easiest and quickest one to solve from the pair. Spare me the agony please...lol

Let's use the bottom one.

x+5y=10
x+5(2)=10
x+10=10
Now, bring the 10 over to the other side switching the sign as well to have the variable x by itself.

x=10-10
so x=0

Now, to take that extra step in finding out if your variables are right. Just use the other equation and plug it in since you have both variables solved.

4x+4y=8
4(0)+4(2)=8
0+8=8
8=8. This is a true statement therefore your answer is correct.

After about a hundred of these problems you'll master it. Good Luck! =)

Answer 5

You solve those equation like this:
4x + 4y =8
To find X you put zero in the y. Like this:
4x + 4(0) = 8.... then the equation is like this now 4x=8.
You now solve for x, by dividing,
x/4=8/4
The result is this x = 2!
Now you solve for Y: 4x+4y = 8
You plug in zero in the X. Like this:
4(0) + 4y = 8.....now the equation is like this 4y = 8
Now you solve for s, by dividing and the answer is y = 2!

For the equation: x + 5y = 10
You do the same thing as the first equation
The answer for X is 10!
The answer for Y is 2!

Answer 6

Solve one of the equation for either x or y. For example, if you solve the first equation for y you will get

4y = 8 - 4x
y = (8-4x)/4 = 2 - x

Now plug the solution for y into the next equation and you will solve numerically for x

x + 5(2-x) = 10
x + 10 -5x = 10
-4x = 0
x = 0

Now that you have solved for x, solve for y in either equation

x + 5y = 10
0 + 5y = 10
5y = 10
y = 2

Answer 7

No, I can't say that helping you was my reason for understanding algebra. I understand it because I've learned it and used it many times. But I'll help anyway.

You have a system of two equations with two unknowns. There are two different ways to go about this.

1) Substitution. Solve one equation for one variable, then plug it into the other. It's easy to solve the second one for x, to get x = 10 - 5y. Plug this into the first equation and you get
4(10 - 5y) + 4y = 8.
Solve this for y. Once you have y, plug it into either of the original equations and solve for x.

2) Adding multiples. Multiply both sides of the equation by -4 to get -4x - 20y = -40. Add this to the first equation to get
-16y = -32. Notice that the "x" disappears, so you can solve this for y. Then once you have y, just like in the previous example you can plug it in to either of the equations and solve for x.

Answer 8

You need to get rid of one of the variables. One way is to multiply one equation by something so one of its variables matches the other. For example 4(x + 5y = 10) -> 4x + 20y = 40. You can then subtract:

4x + 4y = 8
4x + 20y = 40
______________
0 + -16y = -32
y = 2

Plug that back into either formula:

x + 5(2) = 10
x + 10 = 10
x = 0

However this pair of equations gives you an excellent "cheat."
x = 10 - 5y

So you can rewrite the first equation as
4(10 - 5y) + 4y = 8
Then
40 - 20y + 4y =8
40 - 16y = 8
32 = 16y
2 = y

Answer 9

4x + 4y = 8
x + 5y = 10

first we have to delete one of the variables
to do that we have to see that one of the variables is having equal values with opposite sign. to do this we can simply multiply the second equation by -4

that will lead to

4x + 4y = 8
-4x - 20y = -40

so when we deduct first equation from the second we get

-16y = -32
y = -32/-16 = 2

y = 2

to get the value of x simply substitute y in one of the formulas with 2. i am using the first formula

so 4x + (4*2) = 8
4x + 8 = 8
4x = 8 - 8
4x = 0
x = 0/4 = 0.

there for the answers are x = 0 and y = 2

Answer 10

x + 5y = 10
x = 10- 5y

4x + 4y = 8
4(10-5y) + 4y = 8
40 - 20y + 4y = 8
32 = 16y
y = 2

x + 5(2) = 10
x = 0