How can i figure out the answer to; x+4=y and y=3x-8

Question

^{Im so confused, and cannot understand system of linear equations!! please help understand!....}

Answer 1

The other method you can use to solve systems of equations is called elimination or addition.

 

Step one: Write both equations in the same form.

    x-y=-4

-3x+y=-8

 

Step two: Line up the two equations (as above).

Step three: Identify one variable to eliminate through addition or subtraction. Looks like y since you have -y and +y. (Note: The variable will not be eliminated. You are just using a technique to solve the system)

Step 4: Add (or subtract) like you normally would have done with just  numbers when you were first learning how to add and subtract.

That leaves:

-2x +/-(0y)=-12

2x=12

X=6

Now substitute x=6 into the original equations and solve for y.

 

6+4=y

10=y

 

y=3(6)-8

y=18-8

y=10

 

 

Answer 2

Hi Cheyenne--

 

First, put them in the same form (variables in same order):

 

x + 4 = y

3x - 8 = y

 

Then multiply the top equation by 3 (you'll see why in a second...)

 

3x + 12 = 3y

3x  -  8  = y

 

Now you can subtract the bottom from the top to eliminate x:

 

0 + 20 = 2y  (why 20? because "12 minus negative 8" is the same as "12 + 8.")

 

So this means that 20 = 2y, so y by itself is 10.

 

Now plug that into both of the original equations and you'll be able to get x:

 

x + 4 = 10, so x would have to be 6

 

and 10 = 3x -8, so 3x would be 18, and x again would have to be 6. :-)

 

So it's all good.

 

The key in what you just did was to be able to change one equation in such a way that you can then add or subtract whole equations from each other to get rid of one of the variables.

 

Hope that makes sense!

 

All best,

 

Matt in New York

 

 

Answer 3

There are other ways besides graphing to solve systems of linear equations.

 

The basic idea is to reduce the equations so that there is only one unknown.  Once you do that, you can solve for that unknown and use that answer to solve for the other unknown -- assuming there are two unknowns, as in this case.  If there are more unknowns, it's the same idea, but just more complicated.

 

So let's try one method, substitution.  From the second equation you have a way to express y in terms of x.  So if you substitute that expression for y back into the first equation, you can get rid of the y in the first equation.

 

The first equation is x+4 = y

But since y = 3x-8 in the second equation, you can rewrite the first equation as:

 

x + 4 = 3x - 8

 

Now solve for x:

 

Add 8 to both sides:

x + 12 = 3x

 

Subtract x from both sides:

12 = 2x

 

So x = 6, and from the first equation you can see that y must be 10.

 

To check the answer, take these values and try them in the second equation to make sure it's right:

 

y = 3x - 8

10 = 3 * 6 - 8

10 = 18 -8

10 = 10

 

That works, so you know that the answer is correct.  If it didn't work, then you'd know there was a mistake somewhere and you'd have to try it again.

 

 

 

Answer 4

ANSWER: x=6 and y=10

 

The solution is the value for x and the value for y that make both equations equal

 

If you graph both of these equations, they will intersect at one point. The point where they intersect is the solution to this system of equations. 

 

Alternatively, you could solve it by using substitution or elimination. Since these equations are already solved for y, substitution is the easiest method.

 

Take the y value of one of the equations and substitute it into the other equation. So I will take y=3x-8 and substitute that y value into x+4=y and solve the equation for x

 

x+4=3x-8

12=2x; now divide both sides of this equation by two

6=x

x=6

 

So we now know the value for x. Substitute this value of x into either equation to get the value for y. I will use the first equation

 

x+4=y

6+4=y

10=y

y=10

 

And that is your answer. x=6 and y=10