Question

6. Solve by any method:3x - 2y = 6x + y = 2

Answer 1

`\begin{gathered} 3x-2y=6 \\ x+y=2 \end{gathered}`

we can take any equation and solve for any variable, for example y will solve x from the second equation

`\begin{gathered} x+y=2 \\ x=2-y \end{gathered}`

now replace the value of x on the first equation

`\begin{gathered} 3x-2y=6 \\ 3(2-y)-2y=6 \\ \end{gathered}`

simplify

`\begin{gathered} 6-3y-2y=6 \\ 6-5y=6 \end{gathered}`

and solve for y

`\begin{gathered} -5y=6-6 \\ -5y=0 \\ y=(0)/(-5) \\ \\ y=0 \end{gathered}`

Value of y is 0 now we can replace y=0 on any equation and solve for x

for example I will replace y=0 on the second equation to find x

`\begin{gathered} x+y=2 \\ x+(0)=2 \\ x=2 \end{gathered}`

Value of x is 2

If we want to represent the solution as a point, the solution is

`(2,0)`