Question

Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x,y).3x - 2y = -95x + 10y = - 5

Answer 1

Given,

`\begin{gathered} 3x-2y=-9\ldots\ldots\ldots(1) \\ 5x+10y=-5\ldots\ldots\text{.}(2) \end{gathered}`

Multiply 1st equation by 5.

`\begin{gathered} 5(3x-2y=-9) \\ 15x-10y=-45\ldots\ldots\text{.}(3) \end{gathered}`

Solve equations (2) and (3)

`\begin{gathered} 20x=-50 \\ x=(-5)/(2) \end{gathered}`

Put x =-5/2 in equation (1)

`\begin{gathered} 3x-2y=-9 \\ 3*(-5)/(2)-2y=-9 \\ (-15)/(2)-2y=-9 \\ -2y=-9+(15)/(2) \end{gathered}`

Further solved as,

`\begin{gathered} -2y=(-45+15)/(5) \\ -2y=(-30)/(5) \\ -2y=-6 \\ y=3 \end{gathered}`

Therefore, the value of x and y is -5/2 and 3.