Question

I need help with this practiceI am brand new to this type of math, please explain and tutor me step-by-step (with words as well)*I’m also trying to find the most efficient way to solve this Thank you in advance. I’ll be taking notes with a pencil and paper as you work, so please take your time no need in rushing

Answer 1

If 5x=55, x+y=23 and y-z=2 we need to find the value of (2x+y)/z

To get the last value, we need to know the value for each variable, it means we need to know the value for x, the value for y and the value for z.

You have three equations and from these equations, you need to get the values for the variables.

We have the following

`5x=55`
`x+y=23`

and

`y-z=2`

We can notice that almost all the equations have two variables, with exception of the first one. For example, the second one has the variables x and y, and the last equation has the variables y and z. So, the first thing that we are going to do, is to choose the equation which has less variables than the other equations. So we'll work with 5x=55.

To get x apart from the numbers we can divide in both sides by 5, as follows

`5x=55\leftrightarrow(5x)/(5)=(55)/(5)`

Then

`(5x)/(5)=x`

and on the other hand

`(55)/(5)=11`

Then

`x=(5x)/(5)=(55)/(5)=11,\text{ }\leftrightarrow x=11`Now, we've got that x=11.

As we have one value, we need to look for the other equations and try to change the x by its numerical value. We notice that now we only have two equations, the second one and the third one.

`x+y=23`

and

`y-z=2`

Since the third equation doesn't have an x, we need to use the second one, i.e. x+y=23 and put the numerical value for x. Then

`x+y=23\leftrightarrow11+y=23`

Now, once again we get an equation with only one variable, it means that we can solve it.

`11+y=23`

To apart the y from the numbers, we can substract 11 from both sides to get

`11+y-11=23-11`

On the left hand side we get

`11+y-11=y`

and from the right hand side we have

`23-11=12`

Then,

`y=11+y-11=23-11=12\leftrightarrow y=12`Now, we got that y=12.

Now, we only have to solve the last equation,

`y-z=2`

As we found the value for y=12, we can use it to get a new equation and get the value for z.

`y-z=2\leftrightarrow12-z=2`

So, after changing the value of y, we get

`12-z=2`

Once more time, we have gotten an equation with one variable. In this case we are going to apart the z, from the numbers.

The first thing to do is substract 12 from both sides. Then

`12-z-12=2-12`

For the Left hand side we will get

`12-z-12=-z`

and for the right hand side we get

`2-12=-10`

Then

`-z=12-z-12=2-12=-10\leftrightarrow-z=-10`

We've gotten that -z=-10, but we need to get the value for z, so we need to do one step more. In this case, you need to multiply in both sides by -1

`(-1)(-z)=(-1)(-10)`

Then

it means that the value for z is 10. z=10

To get the answer for the expression

`(2x+y)/(z)`

we need to replace the values x=11, y=12, z=10

`(2x+y)/(z)=(2(11)+12)/(10)=(22+12)/(10)=(34)/(10)`

and by simplifying we get that

`(2x+y)/(z)=(34)/(10)=(17)/(5)`So your answer is 17/5