Question

Find the solution of the system of equations.2x – 6y = 86x + 10y = -4

Answer 1

We are to solve for x and y in

`\begin{gathered} 2x\text{ - 6y = 8 ---------1} \\ 6x\text{ + 10y = -4 -------2} \end{gathered}`

We will solve using substitution method

from equation 1

`\begin{gathered} 2x\text{ - 6y = 8} \\ 2x\text{ = 8 + 6y} \\ x\text{ = }\frac{8\text{ + 6y}}{2} \\ x\text{ = }\frac{2(4\text{ + 3y)}}{2} \\ x\text{ = 4 + 3y ----------3} \end{gathered}`

substitute x = 4 + 3y into equation 2

`\begin{gathered} 6x\text{ +10y = -4} \\ 6(4\text{ + 3y) + 10y = -4} \\ 24\text{ + 18y + 10y = -4} \\ 24\text{ + 28y = - 4} \\ 28y\text{ = - 4 - 24} \\ 28y\text{ = -28} \\ y\text{ = }(-28)/(28) \\ y\text{ = -1} \end{gathered}`

substitute y = -1 into equation 3

`\begin{gathered} x\text{ = 4 + 3y} \\ x\text{ = 4 + 3(-1)} \\ x\text{ = 4 - 3} \\ x\text{ = 1} \end{gathered}`

Therefore,

The solution of the system of the equation is

x = 1, y = - 1