Question

Question #61e3e

Answer 1

The system of equations has exactly one solution.
It is the place where the lines intersect, which is at
`x = - (1)/(3)` and `y = (7)/(3)`

Solution: `(`-`(1)/(3), (7)/(3))`

Explanation:

Write the equations so that one of the unknowns has the same coefficient in both equations.

`y - 2x = 3`
`x + y = 2`

1) Write the equations to show that the coefficient of `y` is the same in both equations.
`y - 2x = 3`
`y +   x = 2`

2) Subtract one equation from the other to make the `y` term go to `0` and drop out
`color(white)(....) y - 2x = 3`
`- (y +   x = 2)`
`"-----------------------"`
`color(white)(.....)- 3x = 1`

3) Divide both sides by `-3` to isolate `x`
`x = - (1)/(3)` `larr` answer for `x`

Use the answer for `x` to find the answer for `y`

1) Sub in `- (1)/(3)` in the place of `x` and solve for `y`

`y + x = 2`
`y - (1)/(3) = 2`

2) Add `(1)/(3)` to both sides to isolate `y`

`y = (7)/(3)` `larr` answer for `y`

`color(white)(.............)` . . . . . . . . . . . .

Check

Sub in the values to see if the equation still holds true.
`y - 2x = 3`

`(7)/(3) - (- (2)/(3))` should equal `3`

`(7)/(3)+(2)/(3)` should equal `3`

`(9)/(3)` does equal `3`

`Check!`