Question

Two lines, A and B, are represented by the equations given below:

Line A: 2x + 2y = 8
Line B: x + y = 4

Which statement is true about the solution to the set of equations? (5 points)



It is (8, 4).
It is (4, 8).
There is no solution.
There are infinitely many solutions.

Answer 1

Let's actually find the sol'n set.

Line A: 2x + 2y = 8
Line B: x + y = 4

becomes

 2x + 2y = 8
   x +   y = 4
------------------   Multiply the 2nd equation by -2, obtaining -2x - 2y = -8,         
                         and then add your result to the first equation:

 2x + 2y = 8
-2x - 2y = -8
-------------------   Combine all 3 columns.
  0   +  0  = 0

0 always = 0, so there are infinitely many solutions to this system.

Answer 2

The solution of the set of equations is that there are infinitely many solutions

The equations of the lines are given as:

Line A: 2x + 2y = 8

Line B: x + y = 4

Divide both sides of the equation of line A by 2.

So, we have:

Line A: x + y = 4

Line B: x + y = 4

The above system of equations contains the same equations.

This means that the solution of the set of equations is that there are infinitely many solutions

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