Question

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Line A: 2x + 2y = 8 Line B: x + y = 4 Which statement is true about the solution to the set of equations? It is (8, 4). It is (4, 8). There is no solution. There are infinitely many solutions.

Answer 1

We want to check how many intersections line A and B have, that is, we want to check how many common solutions do these equations have:

i) 2x + 2y = 8

ii) x + y = 4

use equation ii) to write y in terms of x as : y=4-x,

substitute y =4-x in equation i):

2x + 2y = 8
2x + 2(4-x) = 8
2x+8-2x=8
8=8

this is always true, which means the equations have infinitely many common solutions.


Answer: There are infinitely many solutions.