Question

How do you solve x – y = 3 and 2x + 2y = 2?

Answer 1

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

Explanation:

From the first equation, `x=y+3`. Substitute in to the second:
`2(y+3)+2y=2`. Multiply this out: `2y+6+2y=2`. Collect terms: `4y=-4`, so `y=-1`.

Return to the first equation: `x-(-1)=3`, so `x=2`.

Answer 2

`(x,y)to(2,-1)`

Explanation:

`x-y=3to(1)`

`2x+2y=2to(2)`

`"from equation "(1)tox=3+yto(3)`

`"substitute "x=3+y" into equation "(2)`

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

`6+2y+2y=2`

`"subtract 6 from both sides"`

`4y=-4rArry=(-4)/4=-1`

`"substitute "y=-1" into equation "(3)`

`x=3-1=2`

`"point of intersection "=(2,-1)`
graph{(y-x+3)(y+x-1)=0 [-10, 10, -5, 5]}