# Solve each system of equations to the nearest 0.001 for each variable by using a calculator 5F -...

## Question:

Solve each system of equations to the nearest {eq}0.001 {/eq} for each variable by using a calculator

{eq}5F - 2T = 7 {/eq}

{eq}4T + 3F = 8 {/eq}

## Solving the System:

Solving a square system of linear equations we can apply the reduction method, which consists of combining the equations so that we can eliminate a variable in each step.

First rewritten the system:

{eq}\left\{ \begin{array}{l} 5F - 2T = 7\\ 4T + 3F = 8 \end{array} \right. \to \left\{ \begin{array}{l} 5F - 2T = 7\quad \left( 1 \right)\\ 3F + 4T = 8\quad \left( 2 \right) \end{array} \right. {/eq}

Combining the equations we can solve the system:

{eq}3\left( 1 \right) - 5\left( 2 \right)\\ - 26T = - 19\\ T = \frac{{ - 19}}{{ - 26}} \approx 0.731\\ \\ 2\left( 1 \right) + \left( 2 \right)\\ 13F = 22\\ F = \frac{{22}}{{13}} \approx 1.692 {/eq}