Answer:
The System of Equation is Consistent.
Step-by-step explanation:
Given: System of equations y = -x - 13 and y = -3x + 2
To find: System of equation is consistent or inconsistent
System of equation is consistent if it has a unique solution or infinitely many solution and it is in consistent if it has no solution.
So we check if given system of equation has unique solution or infinitely many solution or no solution by checking their ratio.
Rewrite the system of equation,
x + y +13 = 0 and 3x + y - 2 = 0
[tex]a_1=1\:,\:b_1=1\:,\:c_1=13\:and\:a_2=3\:,\:b_2=1\:,\:c_2=-2[/tex]
Now,
[tex]\frac{a_1}{a_2}=\frac{1}{3}[/tex]
[tex]\frac{b_1}{b_2}=\frac{1}{1}[/tex]
[tex]\frac{c_1}{c_2}=\frac{13}{-2}[/tex]
Since, [tex]\frac{a_1}{a_2}\neq\frac{b_1}{b_2}[/tex]
Thus, System of equation has unique solution.
Therefore, The System of Equation is Consistent.
