math help fast?

Question

Well in my math class we are doing substituion and it is very confusing for me one of the problems i have is

8x+2y=13
4x+y=11

Can someone please explian to me how to do this?
Thanks

Answer 1

Sure. When using Substitution the idea is to solve one equation for either variable and then plug that value in for the same variable in the other equation. I'm not going to use your problem, because yours has no solution. I'll explain in a bit. For now, I'll use an example.

If we had:

8x - 2y = 44

and

2x + y = 14

We could use substitution to solve for x and y. It doesn't matter which we do but it looks like solving for y in the second equation would be easiest.

So let's get y by itself by subtracting 2x from both sides like this...

2x (-2x) + y = 14 (-2x)

Simplifying we get...

y = 14 - 2x

Now that we know what y is let's plug that into the other equation.

8x - 2(14 - 2x) = 44

Notice how our value for y (14 - 2x) is in place of y in the second equation. This is what they mean when they say "substitute"

Let's solve...

8x - 2(14 - 2x) = 44

8x - 28 + 4x = 44

12x - 28 = 44

12x = 72

x = 6

Now that we have a value for x let's pick either equation and plug the value in for x. Let's use the second equation again.

2(6) + y = 14

12 + y = 14

y = 2

x = 6, y = 2

That's it. Now let's solve your equation the same way. First solving the second equation for y, again it's just simpler.

4x + y = 11

We'll subtract 4x from both sides.

y = 11 - 4x

Now let's plug this into the other equation for y.

8x + 2(11 - 4x) = 13

8x + 22 - 8x = 13

See here when we combine like terms we cancel out our variables and we're left with 22 = 13, which is not true. Therefore, this problem has no solution.

Hope this helps...Good Luck with your Math.

Answer 2

alright, you want to try to get a variable by itself. So in the second problem you'd subtract 4x

4x+y=11
y=11-4x

Now you take 11-4x and plug it into the other problem as the y term because y=y right? So then it is the same in both of these equations but only in this problem

8x+2y=13
8x+2(11-4x)=13
Group like terms
8x-8x+22=13
22=13 No it doesn't so this answer has no solution.

Answer 3

8x+2y=13
4x+y=11

This would be a false statement, so the answer is

No solution

1.) 8x+2y=13
2.) 4x+y=11

Make equation 2 into y = form and substitute it into equation 1.

y = -4x + 11 substitute it into equation 1.

1.) 8x+2*(-4x +11) =13 solve for x

8x + -8x + 22 = 13 add them up.

22 = 13 Not True , so No solution



Check with another Method

This is called the Elimination Method

1.) 8x+2y=13
2.) 4x+y=11 multiply both sides by a -2.

1.) 8x+2y=13
2.) -8x-2y= -22 add both sides of the equations
------------------------to get the new equation
0 + 0 = -9 new equation

0 = -9, Not true, so no solution.

Answer 4

There are a couple of ways to solve systems of equations, but since you specified substitution, here goes:

Solve the second equation for y, just because it is the easiest one.

y = 11 - 4x

Now go back to the first equation and make that substitution.

8x + 2(11 - 4x)=13

Distribute.

8x + 22 - 8x = 13.

Combine like terms.

22 = 13.

Since 22 does NOT equal 13, it means that there is no solution for this particular system of equations.

Answer 5

well what u need to do is take one of the equations , lets say the second one, and rearrange to get x equals to something 4x + y = 11 will become x = (11-y)/ 4 , then u take this and substitute it in the first equation as the value of x , so like 8 ((11-y)/4) + 2y = 13 , and that will give u a value of y at the end when u solve that equation. u use that y value and substitute it in x = (11-y)/4 and u'll get the value of x. ....and ur done..

Answer 6

Let me let you know what I do to resolve math issues in my head even quicker than with a calculator. First, I learn the solutions given you by way of such a lot and I do not consider their reply goes to be the first-rate one for you. Most persons propose studying math, as with every different field, by way of rote - memorization and recessitation. The crisis with studying by way of rote is that you're discouraged by way of utilising creativity whilst fixing issues. In different phrases, their is a couple of option to resolve a math crisis and academics nowaday best educate pupils methods to study math in a single or 2 approaches. The truth is that there are a few approaches to resolve math issues. For instance: One quantity minus an extra quantity is solved by way of taking the highest quantity and subtracting the backside quantity. That works satisfactory if the equation is 10 minus five. But whilst it's five minus 10, you have got to take the closest quantity to the left, pass it out, and shrink the importance by way of one even as including a one to the importance to the correct. Then subtract the quantity to the correct once more. Hang on with me, ok? Most academics let you know that while you determine your subtraction, that you simply have got to move by way of the crisis two times to determine you reply they usually let you know that over and over again and once more. But now do this: Add the quantity at the backside to the quantity at the reply. If you do it correct, you will have to get the quantity at the most sensible. That is whatever that almost all academics do not educate you given that this can be a inventive reply. Rote goes over the equal crisis two times to look if the reply is the equal. That is why and the way, through the years, I can do regular math in my head FASTER than a calculator. Good success to your reports. Don

Answer 7

look at each equation:

multiply the bottom equation by 2 and get 8x + 2y = 22.

Did you type it in right?

Answer 8

hi,
for system of linear equation say
a1x + b1y = c1
a2x + b2y = c2

have no solution
if (a1/a2) = (b1/b2) != (c1/c2).

It means above system of linear equation represents two parallel line by definition they will never intersect it means above system of linear equation have no solution

Answer 9

I believe you can add them together;
8x+2y=13
4x+y=11
12x+3y=24
AS you have two different unknowns, you cannot go furtther.