Question

Solve the system by any method. Use the Infinity symbol of their infinitely many solutions are entered DNE if there are No solutions4x-10y=-58 And 9x+10y=-14

Answer 1

Solve the system by any method.

`\begin{gathered} 3x-10y=-58 \\ 9x+10y=-14 \end{gathered}`

Using substituttion method:

`\begin{gathered} 3x-10y=-58\ldots\ldots.....(1) \\ 9x+10y=-14\ldots\ldots\ldots\text{.}(2) \\ \text{from equ(1)} \\ 3x-10y=-58 \\ 3x=-58+10y \\ (3x)/(3)=(-58+10y)/(4) \\ \mathrm{Substitute\: }x=(-58+10y)/(3) \end{gathered}`
`\begin{gathered} \text{substitute x} \\ \begin{bmatrix}9\cdot(-58+10y)/(3)+10y=-14\end{bmatrix} \\ \begin{bmatrix}40y-174=-14\end{bmatrix} \\ 40y=-14+174 \\ 40y=160 \\ y=(160)/(40) \\ y=4 \end{gathered}`
`\begin{gathered} x=(-58+10\cdot\:4)/(3) \\ x=x=(-58+40)/(3) \\ x=-(18)/(3) \\ x=-6 \end{gathered}`

Therefore the solution to the system of equation is

`x,y=-6,4`