Question

Solve the system 1/2x+2/3y=1 3/4x-1/3y=3

Answer 1

1/2x+2/3y=1 (1st)
3/4x-1/3y=3 (2nd)

multiply 6 to (1st) equation and 12 to the (2nd) equation

3x + 4y = 6
9x - 4y = 36
------------------add
12x = 42
x = 3.5

3(3.5) + 4y = 6
10.5 + 4y = 6
4y = - 4.5
y = -1.125

answer
solution (3.5 , - 1.125)

Answer 2

Answer:

`((7)/(2) , (-9)/(8) )`

Step-by-step explanation:
To solve the system means to final values of x and y that would satisfy both equations.
To do this, we will need to solve the equations simultaneously.

The first given equation is:

`(1)/(2) x + (2)/(3) y = 1`

Multiply all terms by 6 to get rid of fractions. This will give us:
3x + 4y = 6
This can be rewritten as:
4y = 6 - 3x ..........> equation I

The second given equation is:

`(3)/(4) x - (1)/(3) y = 3`

Multiply all terms by 12 to get rid of the fractions. This will give us:
9x - 4y = 36 .............> equation II

Substitute with equation I in equation II and solve for x as follows:
9x - 4y = 36
9x - (6-3x) = 36
9x - 6 + 3x = 36
12x = 36 + 6
12x = 42
x = 42/12
x = 7/2

Substitute with x in equation I to get y as follows:
4y = 6 - 3x
4y = 6 - 3(7/2)
4y = -9/2
y = -9/8

Based on the above, the solution of the system is:

`((7)/(2) , (-9)/(8) )`