Answer:
-2/9 , 35/9
Explanation:
To solve the system of equations, we can set the two equations equal to each other and solve for $x$:
\begin{align*}
3-4x &= 4+\frac{1}{2}x \\
-\frac{9}{2}x &= 1 \\
x &= -\frac{2}{9}
\end{align*}
Now that we have found $x$, we can substitute it into one of the equations to find $y$:
\begin{align*}
y &= 3-4\left(-\frac{2}{9}\right) \\
y &= \frac{35}{9}
\end{align*}
Therefore, the solution to the system of equations is $\left(-\frac{2}{9},\frac{35}{9}\right)$.
To check if the given points are solutions to the system of equations, we can substitute each point into both equations and see if the equations are satisfied:
\begin{align*}
\text{If } (3.2,5.6): \quad 5.6 &= 3-4(3.2) \quad \checkmark &\quad 5.6 &= 4+\frac{1}{2}(3.2) \quad \checkmark \\
\text{If } (3,5): \quad 5 &= 3-4(3) \quad \checkmark &\quad 5 &= 4+\frac{1}{2}(3) \quad \checkmark \\
\text{If } (-0.22,3.89): \quad 3.89 &= 3-4(-0.22) \quad \checkmark &\quad 3.89 &= 4+\frac{1}{2}(-0.22) \quad \checkmark \\
\text{If } (-1,7): \quad 7 &= 3-4(-1) \quad \checkmark &\quad 7 &= 4+\frac{1}{2}(-1) \quad \checkmark
\end{align*}
All of the given points satisfy both equations, so they are all solutions to the system of equations.