oklahoma algebra

Question

Describe how you would obtain an equation in one variable to solve the system by substitution.

\(x+4y=30\)

\(x=2y\)

Answer 1

Since one equation says x = 2y that means "x" is the same thing as "2y" so in the other equation, wherever an "x" is written, you can plug in "2y"

x + 4y = 30 becomes:

(2y) + 4y = 30

then you can solve for "y" if needed. Once you get the value of "y", you can solve for "x" by using your equation x = 2y

Answer 2

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I know Algebra might be extremely stressful, but I am here to help! I want you to follow this secret recipe to reach the solution for this problem in the easiest possible manner!

1. Since one of the equations is: x=2y, you will use it to substitute for x in the other equation
2. So, the first equation will be: (2y)+4y=30.
3. Now we can solve this equation really easily: (2y)+4y=30 --> 6y=30 --> y=30/6=5
4. Now, you can simply substitute using the obtained y value in any of the initial equations: If we substitute in the first equation: x+4(5)=30 --> x+20=30 --> x=30-20=10

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Answer 3

Given:

Equation 1: x+4y=30

Equation 2: x=2y

You can go about this multiple ways, but the overall point is to create an equation where you are solving for one variable and then use established equations to solve for the other variable.

Route 1: The simplest is that you already have an equation where x=2y. That means you can substitute x in equation 1 with 2y since you already know that x = 2y.

Equation 1 now looks like 2y+4y=30.

This leads to 6y=30, and then by dividing by 6 on both sides you will end up with y=5.

Now you can take the original equation 1 or 2 and plug 5 where there is y and then solve for x.

Using equation 1 you have x+4*5=30.

Simplify to x+20=30. Subtract 20 from either side and you get x=10.

You can use equation 2 to verify that x = 10 and y = 5.

This amounts to 10 = 2*5

Route 2: You can solve for x in equation 1 and substitute it into equation 2.

Starting with equation 1 you have x+4y=30. Subtract 4y from either side and you get x=30-4y

Substitute into equation 2 and you'll have 30-4y=2y. Add 4y to both sides you get 30=6y.

Divide 6 on both sides and you get y=5.

Now plug this into x = 30-4y and you get x = 30-4*5. x =10.

There are many more routes you can take, but typically you want to identify the fastest way to solve.

For example,

Route 3: You can try solving x's value first.

Take equation 2: x=2y and divide 2 on either side. Now you have x/2=y.

Plug this into equation 1: x+4y=30. So you have x+4*(x/2)=30. This simplifies to x+2x=30.

So, 3x =30, which means x=10.

Plugging back into x/2=y. This is now 10/2=y. Therefore, y=5.

Answer 4

x=2y means you can substitute 2y wherever you see an x in the first equation, as they are equivalent. Doing this we see that the x+4y=30 becomes 2y+4y=30

add the y terms to get 6y=30

divide both sides of the equation by 6 to get y=5.

then go back to the second equation x=2y, plug in y=5 to get x=2(5)=10