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} (5v)/(5)=(1)/(5)-(2)/(5)w \\ v=(1)/(5)-(2)/(5)w \end{gathered}`

Second, replace the expression obtained into the first equation:

`\begin{gathered} 2v+6w=-36 \\ 2((1)/(5)-(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(1)/(5)-2\cdot(2)/(5)w+6w=-36 \\ (2)/(5)-(4)/(5)w+6w=-36 \\ (2)/(5)+(26)/(5)w=-36 \end{gathered}`

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

`\begin{gathered} (2)/(5)-(2)/(5)+(26)/(5)w=-36-(2)/(5) \\ (26)/(5)w=-(182)/(5) \end{gathered}`

Multiply both sides by the reciprocal of 26/5

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

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

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

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