# How do you solve the system y=2x-1, 6x-3y=12 by graphing?

Jan 16, 2016

As the two lines have the same slope, they must be either parallel or coincide with one another.

#### Explanation:

For the two straight line curves to cut each other, Their slopes must be different. Let us apply this test first.

1st line

$y = 2 x - 1$

Its slope is the coefficient of $x$ i.e. ${m}_{1} = 2$

2nd equation

It is in the form -

$a x + b y = c$
Its slope is defined by $\frac{- a}{b}$

$6 x - 3 y = 12$
${m}_{2} = \frac{- 6}{- 3} = 2$

As the two lines have the same slope, they must be either parallel or coincide with one another.

Y-intercept of the first line is $\left(0 , 1\right)$

Y-intercept of the 2nd line is $\frac{c}{- b} = \frac{12}{- 3} = - 4$

Since their slopes are the same and intercepts differ, the two lines are parallel to each other.

You can find the intercepts of the two lines.

1st line (0, -1); (0.5,0)
2nd line (0,-4); (2, 0)
Fix the two points each for the two lines
The two lines will be parallel to each other.