128k views
0 votes
Solve the linear system:

(3.2, 5.6)


(3, 5)


(-0.22, 3.89)


(-1, 7)

Solve the linear system: (3.2, 5.6) (3, 5) (-0.22, 3.89) (-1, 7)-example-1
User Jon Topper
by
7.7k points

1 Answer

2 votes

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.

User Cyrus Mohammadian
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.