Asked by Brooke
do the equations y=2x+3 and x=1-2y have common solution, no common solution or infinitely many common solutions?
Answers
Answered by
Henry
Y = 2x + 3
Eq1: -2x + y = 3
X = 1 - 2y
Eq2: x + 2y = 1
Multiply Eq2 by 2 and add Eq1 and Eq2:
-2x + y = 3
+2x + 4y = 2
sum: 5y = 5
Y = 1
In Eq2, replace Y with 1 and solve for x:
x + 2*1 = 1
X = -1.
Solution set: (x,y) = (-1,1).
One common solution.
Eq1: -2x + y = 3
X = 1 - 2y
Eq2: x + 2y = 1
Multiply Eq2 by 2 and add Eq1 and Eq2:
-2x + y = 3
+2x + 4y = 2
sum: 5y = 5
Y = 1
In Eq2, replace Y with 1 and solve for x:
x + 2*1 = 1
X = -1.
Solution set: (x,y) = (-1,1).
One common solution.
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