Question

Solve the given system of equations2x+8y=524x-4y=-15

Answer 1

The equations given are,

`\begin{bmatrix}2x+8y=5..........1 \\ 24x-4y=-15......2\end{bmatrix}`

Isolate 'x' in equation 1

`\begin{gathered} 2x+8y=5 \\ 2x=5-8y \\ x=(5-8y)/(2)...........3 \end{gathered}`

Substitute 'x' is equal to (5-8y)/2 into equation 2

`\begin{gathered} 24\cdot (5-8y)/(2)-4y=-15 \\ -100y+60=-15 \\ -100y=-15-60 \\ -100y=-75 \\ (-100y)/(-100)=(-75)/(-100) \\ y=(3)/(4) \end{gathered}`

Substitute y = 3/4 into equation 3 and solve for x

`\begin{gathered} x=(5-8\cdot (3)/(4))/(2) \\ x=(5-6)/(2) \\ x=-(1)/(2) \end{gathered}`

Hence,

`x=-(1)/(2),\:y=(3)/(4)`