Question

How do you solve `4x - y = 6` and `3x + y = 1`?

Answer 1

`x=1,y=-2`

Explanation:

Notice that when the two equations are added to one another, the `y` and `-y` terms will cancel. This is opportune because we will be left with just `x` terms.

Add the two equations:

`{:(color(white)("(")4x,-y,=6," "),("("3x,+y,=1")",+),(color(white)("(")color(blue)(7x),cancel(+0y),color(blue)(=7)," "):}`

The resulting equation `7x=7` can be divided by `7` on both sides:

`(7x)/7=7/7" "" "=>" "" "color(red)(x=1`

This can be substituted into either equation to solve for `y`. I'll choose the second equation.

`3color(red)x+y=1" "" "=>" "" "3color(red)((1))+y=1`

Solve the resulting equation:

`3+y=1`

`color(green)(y=-2`