SOLUTION: Linear Systems 3. The arms of an angle lie on the lines x+4y=9 and 3x-2y=13. What are the coordinates of the vertex of the angle? pleaseeeeeeeeeeeeeeeee Thank you very much

Question 180765: Linear Systems
3. The arms of an angle lie on the lines x+4y=9 and 3x-2y=13. What are the coordinates of the vertex of the angle?
pleaseeeeeeeeeeeeeeeee
Thank you very much
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the second equation by 2.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

Which form the ordered pair

.

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at

. So this visually verifies our answer.

Graph of (red) and (green)

So from the graph, we see that the vertex of the angle is the point

RELATED QUESTIONS
the vertex of an angle is the point where the lines whose equations are y= 2x and y=x+1... (answered by gonzo)

The sides of an angle are parts of two lines whoes equations are y = -3/2x - 6 and y =... (answered by checkley75)

If the arms of one angle are respectively parallel to the arms of another angle, then the (answered by mananth)

If the two arms of an angle are perpendicular to the two arms of another angle then prove (answered by cleomenius)

A triangle whose sides lie on the lines 1.) 3x + 4y = 8 2.) 3x - 4y = 32 3.) x - 8... (answered by Alan3354)

Find the equation of the circle if a triangle whose sides lie on the lines 3x+4y=8,... (answered by Fombitz)

Find the equation of the circle when a triangle whose sides lie on the lines 3x+4y=-8,... (answered by Fombitz)

Solve the following systems of two linear equations. 2x+4y =18 x+2y... (answered by ewatrrr)

Find the area of the triangle whose sides lie on the graphs of 3x + y + 1 = 0, x + 4y -7... (answered by ikleyn)