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.