Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=1,\:y=-3[/tex]
As the system of equations has only one solution, thus the solution consistent.
Step-by-step explanation:
Given the system of equations
4x - 5y = 19
y = x - 4
Solving the system of equations by using the substitution method.
[tex]\begin{bmatrix}4x-5y=19\\ y=x-4\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=x-4[/tex]
[tex]\begin{bmatrix}4x-5\left(x-4\right)=19\end{bmatrix}[/tex]
[tex]4x-5\left(x-4\right)=19[/tex]
[tex]-x+20=19[/tex]
isolate x for [tex]-x+20=19[/tex]
[tex]-x+20=19[/tex]
[tex]-x=-1[/tex]
Divide both sides by -1
[tex]\frac{-x}{-1}=\frac{-1}{-1}[/tex]
[tex]x=1[/tex]
[tex]\mathrm{For\:}y=x-4[/tex]
[tex]\mathrm{Subsititute\:}x=1[/tex]
[tex]y=1-4[/tex]
[tex]y=-3[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=1,\:y=-3[/tex]
As the system of equations has only one solution, thus the solution consistent.
Please remember that if the system of equations has only one solution, then it is an independent system of equations.
