# How can (1/2)x-5=(1/3)x+6 be set up as a system of equations? answers: a) 2y+x=-10 3y+x=18 b) 2y+2x=-10 3y+3x=18 c) 2y-x=-10 3y-x=18 d) 2y-2x=-10 3y-3x=18

C)

2y-x=-103y-x=18Step-by-step explanation:

Set each side of the equation equal to y, then rearrange to standard form.

(1/2)x -5 = y . . . left side of the equal sign

x -10 = 2y . . . . multiply by 2

-10 = 2y -x . . . . subtract x

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(1/3)x +6 = y . . . right side of the equal sign

x +18 = 3y . . . . . multiply by 3

18 = 3y -x . . . . . subtract x

The corresponding system of equations is ...

2y -x = -103y -x = 18third option.

Step-by-step explanation:

can be rewritten into two separate equationts:

You can observe that this linear equations are written in Slope-Intercept form:

But the equations shown in options provided are written in Standard form:

Therefore, you need to move the x term to the left side of the equation (In each equation):

- For the first equation:

Simplifying:

- For the second equation:

Simplifying:

Then the system of equations is:

(06.01) ⇒ The answer is the listed number 4.

(06.03) ⇒ The answer is C

Step-by-step explanation:

Ok, for the (06.01) what we should do is clear the X so we can later on replace it.

(1) x + 4y = -9

(2) x = -9 -4y (at this point we are moving the 4y to the other side of the equation and since its positive in one side, it goes to the other with a minus on it.)

(3) x = -4y - 9 (all we do here is rearrenge the factors on the right side)

Then we should replace the x in the second equation with (3)

(4) 2x + 5y = −6

(5) 2(−4y − 9) + 5y = −6

And we find the answer thats listed.

(06.03)

First we need to write the equation given.

(1)

Now we work with each side for separate. Since both sides are equal to eachother we can make them equal to y to both sides. And we get this two equations

(2)

(3)

We multiply (2) for 2 in both sides of the equation, to remove the fraction. And we will multiply (3) for 3 in both sides of the equation, to remove the fraction.

And we have this new system of equations.

(4) 2y = x - 10

(5) 3y = x + 18

Now we need to rearrenge the factors, and we will move the x to the left side in both equations, and since both are positive, they pass with a minus sign on it.

So we get.

2y − x = −10

3y − x = 18

Thus the answer is C.

2y-x= -10

3y-x = 18

Step-by-step explanation:

The correct option is . 2y-x = -10 , 3y-x = 18

one half x − 5 = 1/2 (x-5)

one third x + 6 = 1/3 *(x+6)

1/2 x-5 = 1/3x+6 =y

y= 1/2x-5

y = 1/3x+6

Now,

y=x/2 -5 equation 1

y = x/3 +6 equation 2

By taking L.C.M of the first equation we get:

y=x/2 -5

y= x-10/2

Now multiply both terms by 2.

2y=x-10

2y-x= -10

Now lets solve second equation:

Take L.C.M of the second equation:

y = x/3 +6

y=x+18/3

Multiply both sides by 3

3y= x+18

3y-x = 18

Therefore the system of equations we get is:

2y-x= -10

3y-x = 18

Step-by-step explanation:

Set up as a system of equation

To get system of equations, we set each side of the given equation equals to y

Multiply whole equation by 2. That is we multiply each term by 2

Subtract x on both sides

(first equation)

Multiply whole equaiton by 3

Subtract x on both sides

(second equation)

The system of equations is

Step-by-step explanation:

we have

Let set both sides of the equation separately equal to y

so

Left side

Multiply both sides by 2 to remove the fraction

Rewrite as standard equation

-----> equation A

Right side

Multiply both sides by 3 to remove the fraction

Rewrite as standard equation

-----> equation B

therefore

The system of equations is

x + 4y = -9 2x + 5y = -6

x = -4y - 9 plug into the 2x + 5y = -6 in place of the 'x'.

2(-4y -9) + 5y = -6 (The last option).

y = (1/2)(x) - 5 multiply each term by 2 to clear the fraction

2y = x - 10

y = (1/3)(x) + 6 multiply each term by 3 to clear the fraction

3y = x + 18

2y = x - 10 Rearranging 2y - x = -10

3y = x + 18 3y - x = 18

LETTER C

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(1/2) x - 5 = (1/3) x + 6

We can rewrite the equation as a system of equations.

We have then:

y = (1/2) x - 5

y = (1/3) x + 6

a system of equations is

y = (1/2) x - 5

y = (1/3) x + 6