Solved the system by substitution.if the system is inconsistent and has no solution,state this .if the system is dependent,write the form of the solution for any real number x.
x+y=50
0.25x+0.75y=0.60(50)

Question

Solved the system by substitution.if the system is inconsistent and has no solution,state this .if the system is dependent,write the form of the solution for any real number x. 
x+y=50
0.25x+0.75y=0.60(50)

mathstudent55 · Answer

Are you familiar with the substitution method?

anonymous · Answer

I am not thats why I need help

mathstudent55 · Answer

Ok, no problem.
The substitution method is the following:
1. Solve one equation for one variable.
2. Substitute what that variable is equal to in the other equation.
Now you have one equation in one variable, so you can find the value of one variable.
3. Substitute the value of the known variable in one of the original equations to find the other variable.

anonymous · Answer

Can you solved this so as I can learn from it

mathstudent55 · Answer

Ok, now let's go through each step and do it together.

anonymous · Answer

Ok good

mathstudent55 · Answer

1. Let's solve the first equation for x.
$x + y=50$

mathstudent55 · Answer

We subtract y from both sides to get:

$x = 50 - y$

mathstudent55 · Answer

That takes care of step 1.

2. Now we substitute what x is equal to in the second equation.

mathstudent55 · Answer

Here is the second equation. We will insert 50 - y for x, and we can also multiply out the right side.

$0.25x+0.75y=0.60(50)$

$0.25(50 - y) + 0.75y=30$

mathstudent55 · Answer

Now we have one equation in one variable, so we solve it for y.

mathstudent55 · Answer

$0.25(50 - y) + 0.75y=30$

Distribute the 0.25:

$12.5 - 0.25y + 0.75y = 30 $

Combine like terms on the left side:

$12.5 + 0.5y = 30 $

Subtract 12.5 from both sides:

$0.5y = 17.5$

anonymous · Answer

How did you get 30

mathstudent55 · Answer

Divide both sides by 0.5:

$y = 35$

mathstudent55 · Answer

Look at the first line that has 30 in it, and then look at the line just above.

anonymous · Answer

Oh Ok

anonymous · Answer

is  the system  inconsistent and has no solution,or dependent

mathstudent55 · Answer

30 is simply 0.60 * 50

anonymous · Answer

the system is inconsistent and has no solution,state this .if the system is dependent

mathstudent55 · Answer

Now we move on to step 3.
Since we know that y = 35, we substitute y with 35 in one of the two original equations.
Let's use the first equation:

$x + y = 50$

$x + 35 = 50$

Subtract 35 from both sides to get:

$x = 15$

The final answer is: the solution is x = 15 and y = 35.

anonymous · Answer

so its a solution

mathstudent55 · Answer

Yes. This system has one solution. It is not inconsistent, and it is not dependent.

anonymous · Answer

I have any equation 9x+4y=23
                             
5x-2y=-2

anonymous · Answer

But let me solved it first

mathstudent55 · Answer

ok

anonymous · Answer

9x+4y=23
5x-2=-2
5(23-4y)-2=-2
115-20-2=-2
115-22=-2
-22=-2
-22y=-117
=5.31

mathstudent55 · Answer

Not quite.
Remember, you must solve one equation for one variable.

It looks like you were trying to solve the first equation for x, to then insert in the second equation.

Let's do that together.

anonymous · Answer

Ok good but am trying

mathstudent55 · Answer

Solve for x:

9x+4y=23

First, we subtract 4y from both sides:

9x = 23 - 4y This is what you got.
It is correct up to here, but you have not solved the equation for x. You only have 9x so far. You need one more step. You need to divide both sides by 9.

$x = \dfrac{23}{9} - \dfrac{4}{9}y$

Now it is solved for x.

mathstudent55 · Answer

I see you are tryong. It was a good effort. Now we will iron out the problems.

mathstudent55 · Answer

Now that we have one equation solved for x, we insert what x is equal to in the other equation. This is the "substitution" step, and what gives this method the name "substitution method."

mathstudent55 · Answer

x is equal to the quantity in red.

$x = \color{red}{\dfrac{23}{9} - \dfrac{4}{9}y}$

Here is the second equation.

$5\color{red}{x}-2y=-2$

In the next step, we'll replace the red x by the red quantity.

$5 \left(\color{red}{\dfrac{23}{9} - \dfrac{4}{9}y} \right) - 2y = -2$

mathstudent55 · Answer

Now we need to solve that equation for y.

anonymous · Answer

How did we solved for Y

mathstudent55 · Answer

We distribute the 5:

$ \dfrac{115}{9} - \dfrac{20}{9}y - 2y = -2 $

anonymous · Answer

5x23=115

anonymous · Answer

5x4=20

mathstudent55 · Answer

Since we have a denominator of 9 on the left side, we multiply the entire equation by 9:

$ 9\left[\dfrac{115}{9} - \dfrac{20}{9}y - 2y \right]= 9(-2)$

$115 - 20y - 18y = -18 $

$115 - 38y = -18$

$-38y = -133$

$y = 3.5$

mathstudent55 · Answer

Now that we have y = 3.5, we substitute that value into the first equation:

$9x + 4y = 23$

$9x + 4(3.5) = 23 $

$9x + 14 = 23$

$9x = 9$

$x = 1$

mathstudent55 · Answer

The solution is x = 1 and y = 3.5.

anonymous · Answer

How did you get 14

mathstudent55 · Answer

4 times 3.5 = 14

anonymous · Answer

Oh great is the system is inconsistent and has no solution,state this .if the system is dependent

mathstudent55 · Answer

If you get a solution, that means the system is not inconsistent or dependent.

anonymous · Answer

Ok thanks

anonymous · Answer

I have two equation but they are in word problem ...same equation

mathstudent55 · Answer

Start a new post for each question.

anonymous · Answer

Ok