How do you solve #3x - y = 3#, #2x + y = 2# by graphing and classify the system?

1 Answer
Aug 27, 2017

Answer:

See a solution process below:

Explanation:

For each equation we need to solve for two points which solve the equation and plot these points and then draw a line through the points:

Equation 1:

First Point:
For #x = 0#

#(3 * 0) - y = 3#
#0 - y = 3#
#-y = 3#
#color(red)(-1) * -y = color(red)(-1) * 3#
#y = -3# or #(0, -3)#

Second Point:
For #y = 0#

#3x - 0 = 3#
#3x = 3#
#(3x)/color(red)(3) = 3/color(red)(3)#
#x = 1# or #(1, 0)#

graph{(3x-y-3)(x^2+(y+3)^2-0.075)((x-1)^2+y^2-0.075)=0 [-20, 20, -10, 10]}

Equation 2:

First Point:
For #x = 0#

#(2 * 0) + y = 2#
#0 + y = 2#
#y = 2# or #(0, 2)#

Second Point:
For #y = 0#

#2x + 0 = 2#
#2x = 2#
#(2x)/color(red)(2) = 2/color(red)(2)#
#x = 1# or #(1, 0)#

graph{(2x+y-2)(3x-y-3)(x^2+(y-2)^2-0.075)((x-1)^2+y^2-0.075)=0 [-20, 20, -10, 10]}

We can see the points cross at #(1, 0)#

graph{(2x+y-2)(3x-y-3)((x-1)^2+y^2-0.05)=0 [-10, 10, -5, 5]}

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent.

This system is an independent consistent system.