Question

4. Solve the system of equations without graphing. *2v + 6w = -365v + 2w = 1

Answer 1

Given the equation system:

$\begin{gathered} 2v+6w=-36 \\ 5v+2w=1 \end{gathered}$

To solve the equation system, you can use the substitution method.

First, write one of the equations for one of the variables, for example, write the second equation for v:

$5v+2w=1$

Pass 2w to the right side of the equation by applying the opposite operation to both sides of it:

$\begin{gathered} 5v+2w-2w=1-2w \\ 5v=1-2w \end{gathered}$

Divide both sides by 5

$\begin{gathered} \frac{5v}{5}=\frac{1}{5}-\frac{2}{5}w \\ v=\frac{1}{5}-\frac{2}{5}w \end{gathered}$

Second, replace the expression obtained into the first equation:

$\begin{gathered} 2v+6w=-36 \\ 2(\frac{1}{5}-\frac{2}{5}w)+6w=-36 \end{gathered}$

Now you have to solve the expression for w:

Distribute the multiplication on the parentheses term:

$\begin{gathered} 2\cdot\frac{1}{5}-2\cdot\frac{2}{5}w+6w=-36 \\ \frac{2}{5}-\frac{4}{5}w+6w=-36 \\ \frac{2}{5}+\frac{26}{5}w=-36 \end{gathered}$

Subtract 2/5 to both sides of the equal sign:

$\begin{gathered} \frac{2}{5}-\frac{2}{5}+\frac{26}{5}w=-36-\frac{2}{5} \\ \frac{26}{5}w=-\frac{182}{5} \end{gathered}$

Multiply both sides by the reciprocal of 26/5

$\begin{gathered} (\frac{26}{5}\cdot\frac{5}{26})w=(-\frac{182}{5})(\frac{5}{26}) \\ w=-7 \end{gathered}$

Once you determine the value of w, you can calculate the value of v

$\begin{gathered} v=\frac{1}{5}-\frac{2}{5}w \\ v=\frac{1}{5}-\frac{2}{5}(-7) \\ v=\frac{1}{5}+\frac{14}{5} \\ v=\frac{15}{5}=3 \end{gathered}$

The solution of the equation system is w=-7 and v=3