Question

Using the elimination method, what is the ordered pair 3x - 6y = 5 3x - 6y = 6?

Answer 1

`"no solution"`

Explanation:

`"the left side of both equations are identical"`
`"thus subtracting them will eliminate both x"`
`"and y terms"`

`"expressing both equations in "color(blue)"slope-intercept form"`

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`3x-6y=5rArry=1/2x-5/6`

`3x-6y=6rArry=1/2x-1`

`"both lines have the same slope and are therefore"`
`"parallel lines with no intersection"`

`"hence the system has no solution"`
graph{(y-1/2x+5/6)(y-1/2x+1)=0 [-10, 10, -5, 5]}

Answer 2

As both the equations have same value on L H S but different values on R H S, the equations are inconsistent and hence no solution.

Explanation:

As both the equations have same value on L H S but different values on R H S, the equations are inconsistent and hence no solution.