If you try to solve it by the substitution method:
Solve the first equation for y
x + y = 7
y = 7 - x
Substitute y = 7 in the second equation:
2x + 2y = 14
2x + 2(7 - x) = 14
2x + 14 - 2x = 14
14 = 14
The x's canceled out and left a true numerical equation 14 = 14.
So it is a dependent system. It has infinitely many solutions.
For instance
1. x=3, y=4, the ordered pair (x,y) = (3,4) is a solution:
Checking in the first Checking in the second
equation: equation:
x + y = 7 2x + 2y = 14
3 + 4 = 7 2(3) + 2(4) = 14
7 = 7 6 + 8 = 14
14 = 14
2. x=2, y=5, the ordered pair (x,y) = (2,5) is a solution:
Checking in the first Checking in the second
equation: equation:
x + y = 7 2x + 2y = 14
2 + 5 = 7 2(2) + 2(5) = 14
7 = 7 4 + 10 = 14
14 = 14
3. x=-3, y=10, the ordered pair (x,y) = (-3,10) is a solution:
Checking in the first Checking in the second
equation: equation:
x + y = 7 2x + 2y = 14
-3 + 10 = 7 2(-3) + 2(10) = 14
7 = 7 -6 + 20 = 14
14 = 14
I could show you thousands and thousands of solutions because the
two equations have the same line as a graph, and so they have ALL
points in common.
Answer: {(x,y)|y = 7-x} dependent system
Edwin
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