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

2 Answers
Jun 14, 2018

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

Explanation:

From the first equation, x=y+3x=y+3. Substitute in to the second:
2(y+3)+2y=22(y+3)+2y=2. Multiply this out: 2y+6+2y=22y+6+2y=2. Collect terms: 4y=-44y=4, so y=-1y=1.

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

Jun 14, 2018

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

Explanation:

x-y=3to(1)xy=3(1)

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

"from equation "(1)tox=3+yto(3)from equation (1)x=3+y(3)

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

2(3+y)+2y=22(3+y)+2y=2

6+2y+2y=26+2y+2y=2

"subtract 6 from both sides"subtract 6 from both sides

4y=-4rArry=(-4)/4=-14y=4y=44=1

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

x=3-1=2x=31=2

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