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.