Answer:
The solution is:
[tex]y=7,\:x=3[/tex]
Step-by-step explanation:
I think substitution method would be the best method for solving the given system of equations.
The reason is that all we need is to plug in the the value of y i.e. y=x+4 in the equation 3x – 4y = -19, then solve for x, and in the end substitute the value x in the equation y=x+4 to get the y-value.
The other method, elimination method, can also be used, but elimination method in current system of the equations would involve a certain degree of arrangements of the variables and then different multiplying of the equation to eliminate the variables.
Thus, I think substitution method would be the best method for solving the given system of equations.
Let us solve using substitution method
[tex]\begin{bmatrix}y=x+4\\ 3x-4y=-19\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=x+4[/tex]
[tex]\begin{bmatrix}3x-4\left(x+4\right)=-19\end{bmatrix}[/tex]
[tex]\begin{bmatrix}-x-16=-19\end{bmatrix}[/tex]
[tex]x=-16+19[/tex]
[tex]x=3[/tex]
Now, just substitute x=3 in y=x+4
[tex]y=x+4[/tex]
[tex]y=3+4[/tex]
[tex]y=7[/tex]
Thus, the solution is:
[tex]y=7,\:x=3[/tex]
