Answer:
[tex] (\frac{7}{2} , \frac{-9}{8} )[/tex]
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:
[tex] \frac{1}{2} x + \frac{2}{3} y = 1[/tex]
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:
[tex] \frac{3}{4} x - \frac{1}{3} y = 3[/tex]
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:
[tex] (\frac{7}{2} , \frac{-9}{8} )[/tex]
