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

1 Answer
Jan 16, 2016

Answer:

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=2x-1#

Its slope is the coefficient of #x# i.e. #m_1=2#

2nd equation

It is in the form -

#ax+by=c#
Its slope is defined by #(-a)/b#

#6x-3y=12#
#m_2=(-6)/(-3)=2#

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

To have an idea about this, Find their respective Y-intercepts.

Y-intercept of the first line is #(0, 1)#

Y-intercept of the 2nd line is #c/(-b)=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.

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