Question

Find the solution of this system of linearequations. Separate the x- and y- values with acomma. Enclose them in a pair of parantheses. System of equations4x + 8y = 838x + 7y = 76- 8x - 16y = -1668x + 7y = 76

Answer 1

Given,

System of equation is,

`\begin{gathered} 4x+8y=83\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}`

Taking the equation (i) as,

`\begin{gathered} 4x+8y=83 \\ 4x=83-8y \\ x=(83-8y)/(4) \end{gathered}`

Substituting the value of x in equation (ii) then,

`\begin{gathered} 8x+7y=76 \\ 8((83-8y)/(4))+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}`

Substituting the value of y in above equation then,

`\begin{gathered} x=(83-8*10)/(4) \\ x=(3)/(4) \end{gathered}`

Hence, the value of x is 3/4 and y is 10. (3/4, 10)

System of equation is,

`\begin{gathered} -8x-16y=-166\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}`

Taking the equation (i) as,

`\begin{gathered} -8x-16y=-166 \\ 8x+16y=166 \\ 4x+8y=83 \\ 4x=83-8y \\ x=(83-8y)/(4) \end{gathered}`

Substituting the value of x in equation (ii) then,

`\begin{gathered} 8x+7y=76 \\ 8((83-8y)/(4))+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}`

Substituting the value of y in above equation then,

`\begin{gathered} x=(83-8*10)/(4) \\ x=(3)/(4) \end{gathered}`

Hence, the value of x is 3/4 and y is 10. (3/4, 10)