Does anyone know an easy way of solving systems of linear equations graphically and numerically?  Please help and see an example below.  Thank you in advance.Solve the system of linear...

Does anyone know an easy way of solving systems of linear equations graphically and numerically?  Please help and see an example below.  Thank you in advance.

Solve the system of linear equations:

y=2x

3x-y=-2

Asked on by jewel2005

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

You pick any value of x ... 1, 2, -1, 0, .... just any value and then ypu subsitute into the euqation of the line to find the y-coordinate.

 

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

You do not need to find the intersection point. First you will need to find two two points on each line and then draw a line through these points. The lines will meet at the intersection points.

For example.

y= 2x

We will find two points on the graph.

==> let x= 1 ==> y = 2*1 = 2==> (1,2) is on the graph.

==> let y= 0 ==> y= 0 ==> The point (0,0) is on the graph too.

Now we will find the points on the graph and then connect between them with a line that we can extend far from the points.

The same for the line 3x-y = -2

==> let x= 1 ==> 3 -y= -2 ==> y= 5 ==> (1,5) on the graph.

==> x= 0 ==> y= 2 ==> (0,2) is on the graph.

Now we can draw a line between those points.

 

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equations:

y= 2x

3x -y= -2

To solve numerically, we will substitute with y= 2x in the equation 3x-y = -2

==> 3x -y = -2

==> 3x - (2x) = -2

==> 3x -2x = -2

==> x = -2

Now we will substitute in y= 2x to find y.

==> y= 2x = 2*-2 = -4

Then the solution is the point (-2, -4)

 

To solve graphically, we need to draw each line and find the point of intersection between both lines.

==> y= 2x  ( Black line)

==> 3x-y=-2 (red line)

We notice that the lines intersect at the point (-2, -4).

 

jewel2005's profile pic

jewel2005 | (Level 2) Honors

Posted on

How are you finding the two points? What equation or method are you using to find the coordinates of the lines?  Im sorry...So confused. :-\

jewel2005's profile pic

jewel2005 | (Level 2) Honors

Posted on

OK...Thanks.  I now know how to find the points of intersection...but I am still having trouble figuring out how the two lines are placed on the graph.  I can find the point of intersection on the graph, but can figure out from which way the lines go through the point of intersection.

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