Answer: It is consistent as the lines are intersecting lines and it has a unique solution
Step-by-step explanation:
Since we have given two systems of equation :
[tex]y=4x-4\\\\and\\\\y=4x+4[/tex]
We need to check whether the system of equations is consistent or inconsistent.
As we know the formula for checking the consistency :
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
In first equation we have
[tex]y=4x-4\\\\4x-y=4\\\\Here,a_1=4,b_1=-1,c_1=4[/tex]
similarly,
In the second equation we have
[tex]y=-4x+4\\\\4x+y=4\\\\Here,a_2=4,b_2=1,c_2=4[/tex]
So, According to question, we have
[tex]\frac{1}{4}\neq \frac{1}{-1}\neq \frac{4}{4}\\\\0.25\neq -1\neq 1[/tex]
Hence, it is consistent as the lines are intersecting lines and it has a unique solution.
Answer:
The given system of equations is consistent.
Step-by-step explanation:
The given equations are
[tex]y=4x-4[/tex] (1)
[tex]y=-4x+4[/tex] (2)
Add both equations,
[tex]2y=0[/tex]
[tex]y=0[/tex]
Put this value in 1.
[tex]0=4x-4[/tex]
[tex]x=1[/tex]
Using the elimination method the solution of given equations is (1,0).
Since the system of equations has a solution, therefore the given system of equations is consistent.
