elimination problem
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Problem: use elimination to solve this system of equations 3x+6y=7 2x+4y=22
elimination problem

1) 3x + 6y = 7
2) 2x + 4y = 22

Multiply equation 1 by 2.

2(3x + 6y) = 7 * 2
3) 6x + 12y = 14

Multiply equation 2 by 3.

3(2x + 4y) = 22 * 3
4) 6x + 12y = 66

Subtract equation 3 from equation 4.

  6x + 12y = 66
-(6x + 12y = 14)
-----------------
  0x +  0y = 52

We have an impossibility here.
Re-write both equations in slope-intercept form.

1) 3x + 6y = 7
6y = -3x + 7
y = -1/2 x + 7/6

 

2) 2x + 4y = 22
4y = -2x + 22
y = -1/2 x + 5.5

Both equations have the same slope. They represent
parallel lines. There is no intersection for these
two lines, therefore, there is no solution to the system.
by Level 11 User (78.4k points)

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