Question

2x + y = 3

x - 2y = -1

If equation one is multiplied by 2 and then the equations are added, the result is _____.

Answer 1

4x+2y=6
+
x-2y=-1

5x=5
x=1

Answer 2

If equation one is multiplied by 2 and then the equations are added, the result is x=1.

Explanation:

The first equation is given by:

`2x+y=3`

and the second equation is given by:

`x-2y=-1---------(2)`

Now on multiplying first equation by 2 we get:

`4x+2y=6---------(1)`

and now on adding this equation to equation (2) we get:

`4x+2y+(x-2y)=6-1\\\\i.e.\\\\4x+2y+(x-2y)=5`

Now on combining the like terms we get:

`4x+x+2y-2y=5\\\\i.e.\\\\5x=5\\\\i.e.\\\\x=(5)/(5)\\\\i.e.\\\\x=1`

and on putting the value of x back to the equation (2) we get:

`y=1`