To solve the first equation, we first simplify the terms on the left side:
[tex] \frac{1}{3} (x - 4) + 6x = 5 - 1 \frac{1}{2} [/tex][tex] \frac{1}{3}x - \frac{4}{3} + 6x = 5 - \frac{3}{2} [/tex][tex] \frac{1}{3}x + 6x = \frac{10}{2} - \frac{3}{2} + \frac{4}{3} [/tex][tex] \frac{1}{3}x + 6x = 5 - \frac{3}{2} + \frac{4}{3} [/tex][tex] \frac{1}{3}x + 6x = 5 - \frac{3}{2} + \frac{4}{3} [/tex][tex] \frac{1}{3}x + 6x = 5 - 1.5 + \frac{4}{3} [/tex][tex] \frac{7}{3}x = 3.5 + \frac{4}{3} [/tex][tex] \frac{7}{3}x = 3.5 + 1.33 [/tex][tex] \frac{7}{3}x = 4.83 [/tex][tex] x = \frac{4.83 \times 3}{7} [/tex][tex] x = 2.07 [/tex]
Now, let's solve the second equation:
[tex] 3.2(1 - 2y) = 0.7(3y + 1.5) [/tex][tex] 3.2 - 6.4y = 2.1y + 1.05 [/tex][tex] 3.2 - 1.05 = 2.1y + 6.4y [/tex][tex] 2.15 = 8.5y [/tex][tex] y = \frac{2.15}{8.5} [/tex][tex] y = 0.253 [/tex]
Therefore, the solutions to the system of equations are [tex] x = 2.07[/tex] and [tex] y = 0.253[/tex].
To solve the first equation, we first simplify the terms on the left side:
[tex] \frac{1}{3} (x - 4) + 6x = 5 - 1 \frac{1}{2} [/tex]
[tex] \frac{1}{3}x - \frac{4}{3} + 6x = 5 - \frac{3}{2} [/tex]
[tex] \frac{1}{3}x + 6x = \frac{10}{2} - \frac{3}{2} + \frac{4}{3} [/tex]
[tex] \frac{1}{3}x + 6x = 5 - \frac{3}{2} + \frac{4}{3} [/tex]
[tex] \frac{1}{3}x + 6x = 5 - \frac{3}{2} + \frac{4}{3} [/tex]
[tex] \frac{1}{3}x + 6x = 5 - 1.5 + \frac{4}{3} [/tex]
[tex] \frac{7}{3}x = 3.5 + \frac{4}{3} [/tex]
[tex] \frac{7}{3}x = 3.5 + 1.33 [/tex]
[tex] \frac{7}{3}x = 4.83 [/tex]
[tex] x = \frac{4.83 \times 3}{7} [/tex]
[tex] x = 2.07 [/tex]
Now, let's solve the second equation:
[tex] 3.2(1 - 2y) = 0.7(3y + 1.5) [/tex]
[tex] 3.2 - 6.4y = 2.1y + 1.05 [/tex]
[tex] 3.2 - 1.05 = 2.1y + 6.4y [/tex]
[tex] 2.15 = 8.5y [/tex]
[tex] y = \frac{2.15}{8.5} [/tex]
[tex] y = 0.253 [/tex]
Therefore, the solutions to the system of equations are [tex] x = 2.07[/tex] and [tex] y = 0.253[/tex].