How do you solve #3x - y = 3#, #2x + y = 2# by graphing and classify the system?
1 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
Second Point:
For
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
Second Point:
For
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
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.