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

Oct 1, 2017

$\text{no solution}$

#### Explanation:

$\text{the left side of both equations are identical}$
$\text{thus subtracting them will eliminate both x}$
$\text{and y terms}$

$\text{expressing both equations in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$3 x - 6 y = 5 \Rightarrow y = \frac{1}{2} x - \frac{5}{6}$

$3 x - 6 y = 6 \Rightarrow y = \frac{1}{2} x - 1$

$\text{both lines have the same slope and are therefore}$
$\text{parallel lines with no intersection}$

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

Oct 13, 2017

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.