Question

The system of equations may be solved by hand calculation or by using the crossing-graphs method.Solve the system of equations shown below by hand calculation.5x - y = 04x + 5y = 116(x, y) =(_____,______)

Answer 1

You have the following System of equations:

`\mleft\{\begin{aligned}5x-y=0 \\ 4x+5y=116\end{aligned}\mright.`

You can solve it by using the Elimination method. The steps are:

1. In order to remove one of the variables, you can multiply the first equation by 5 and then add the equations:

`\begin{gathered} \mleft\{\begin{aligned}25x-5y=0 \\ 4x+5y=116\end{aligned}\mright. \\ _(---------------) \\ 29x=116 \end{gathered}`

2. Solve for "x":

`\begin{gathered} x=(116)/(29) \\ x=4 \end{gathered}`

3. Substitute the value of "x" into the first equation and solve for "y":

`\begin{gathered} 5x-y=0 \\ 5(4)-y=0 \\ 20-y=0 \\ -y=-100 \\ y=20 \end{gathered}`

Therefore, the solution is: