`3x - y = 9, x - 2y = -2` Solve the system of linear equations and check any solutions algebraically.

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`3x-y=9`

`x-2y=-2`

From the second equation,

`x=-2+2y`

Substitute the above expression of x in the first equation,

`3(-2+2y)-y=9`

`-6+6y-y=9`

`-6+5y=9`

`5y=9+6`

`5y=15`

`y=15/5`

`y=3`

Plug the value of y in the expression,

`x=-2+2y`

`x=-2+2*3`

`x=-2+6`

`x=4`

Now let's check the solution by plugging in the equations,

Plug in the solutions...

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`3x-y=9`

`x-2y=-2`

From the second equation,

`x=-2+2y`

Substitute the above expression of x in the first equation,

`3(-2+2y)-y=9`

`-6+6y-y=9`

`-6+5y=9`

`5y=9+6`

`5y=15`

`y=15/5`

`y=3`

Plug the value of y in the expression,

`x=-2+2y`

`x=-2+2*3`

`x=-2+6`

`x=4`

Now let's check the solution by plugging in the equations,

Plug in the solutions in the first equation,

`3*4-3=9`

9=9

Plug in the solution in the second equation,

`4-2*3=-2`

`4-6=-2`

`-2=-2`

Solutions satisfy both the equations

Hence the solutions of the equations are x=4 and y=3

 

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