How do you solve the system by graphing and what is the ordered pair for x - 2y = 0 and 5x+2y=24?

1 Answer
smendyka
Aug 20, 2017

See a solution process below:

Explanation:

For each equation we can find two solutions for the equation, plot the points and draw a line through the two points to graph the line.

Equation 1

For #x = 0#

#0 - 2y = 0#

#-2y = 0#

#(-2y)/color(red)(-2) = 0/color(red)(-2)#

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

For #x = 4#

#4 - 2y = 0#

#-color(red)(4) + 4 - 2y = -color(red)(4) + 0#

#0 - 2y = -4#

#-2y = -4#

#(-2y)/color(red)(-2) = (-4)/color(red)(-2)#

#y = 2# or #(4, 2)#

graph{(x^2+y^2-0.25)((x-4)^2+(y-2)^2-0.25)(x-2y)=0 [-30, 30, -15, 15]}

Equation 2

For #x = 0#

#(5 * 0) + 2y = 24#

#0 + 2y = 24#

#2y = 24#

#(2y)/color(red)(2) = 24/color(red)(2)#

#y = 12# or #(0, 12)#

For #x = 2#

#(5 * 2) + 2y = 24#

#10 + 2y = 24#

#-color(red)(10) + 10 + 2y = -color(red)(10) + 24#

#0 + 2y = 14#

#2y = 14#

#(2y)/color(red)(2) = 14/color(red)(2)#

#y = 7# or #(2, 7)#

graph{(x^2+(y-12)^2-0.25)((x-2)^2+(y-7)^2-0.25)(5x+2y-24)(x-2y)=0 [-30, 30, -15, 15]}

Solution

We can see below the lines intersect at: (4, 2)

graph{(5x+2y-24)(x-2y)=0 [-12, 12, -6, 6]}

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