Solve for the system of equations x/3+2/3=y/6 x/12-y/4=3/2 I need help asap Thank you :)

The ordered pair (-6, -8)

This means x = -6 and y = -8 pair up together

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Explanation:

x/3+2/3=y/6  is equivalent to 2x+4 = y after multiplying both sides by the LCD 6. Multiplying both sides by the LCD always clears out the fractions.

Do a similar operation to x/12-y/4 = 3/2 to get x-3y = 18. The LCD in that case is 12.

The original system

turns into

after clearing out the fractions. From here, we can use substitution to solve this equivalent system. The first equation 2x+4 = y is the same as y = 2x+4. We can replace every copy of 'y' in the second equation and solve for x like so...

x - 3y = 18

x - 3( y ) = 18

x - 3( 2x+4 ) = 18 ... y replaced with 2x+4

x - 3(2x) - 3(4) = 18

x - 6x - 12 = 18

-5x - 12 = 18

-5x = 18+12

-5x = 30

x = 30/(-5)

x = -6

Which is then used to find y

y = 2x+4

y = 2(-6)+4

y = -12+4

y = -8

Put together, the solution is the ordered pair (x,y) = (-6, -8)

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We can check this through graphing and noting the two lines cross at (-6,-8)

Or we can plug (x,y) = (-6,-8) back into each original equation

Let's do the first equation

x/3 + 2/3 = y/6

-6/3 + 2/3 = -8/6

-6/3 + 2/3 = -4/3

(-6+2)/3 = -4/3

-4/3 = -4/3 ... first equation is confirmed

Now onto the second equation

x/12 - y/4 = 3/2

-6/12 - (-8)/4 = 3/2

-1/2 + 4/2 = 3/2

(-1+4)/2 = 3/2

3/2 = 3/2 .... second equation is confirmed as well

Both equations are true when we plug in (x,y) = (-6, -8) so the answer is confirmed overall.

x = - 6 ; y = - 8

Step-by-step explanation:

In the first linear eqn. in 2 variable ,

Simplifying the above eqn. gives =

From eqn.1 value of x in terms of y =

Now in the second linear eqn. in 2 variable ,

Simplifying the above eqn. gives =

Substituting the value of x in eqn.2 gives

Putting the value of y in eqn.1 gives =