How do you solve the system of equations graphing #x=5, 4x+5y=20#?

Question

1871 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-20T12:49:55

See a solution process below:

The equation #x = 5# is a vertical line. For each and every value of #y#, #x# will always be #5#. We can graph this as:

graph{0.00000000000000001y-x+5=0}

Now, we can find two points from the equation for the second line to plot and draw a line through them to graph the second line.

For #x = 0#

#(4 * 0) + 5y = 20#

#0 + 5y = 20#

#5y = 20#

#(5y)/color(red)(5) = 20/color(red)(5)#

#y = 4# or #(0, 4)#

For #y = 0#

#4x + (5 * 0) = 20#

#4x + 0 = 20#

#4x = 20#

#(4x)/color(red)(4) = 20/color(red)(4)#

#x = 5# or #(5, 0)#

graph{(4x+5y-20)((x-5)^2+y^2-0.125)(x^2+(y-4)^2-0.125)(0.00000000000000001y-x+5)=0}

We can see the lines intersect at #(5, 0)# which is the solution.