Answer:
B. [tex](5,-4)[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to find he solution for our given system.
[tex]4x+y=16...(1)[/tex]
[tex]2x+3y=-2...(2)[/tex]
We will use substitution method to solve our given system. From equation (1) we will get:
[tex]y=16-4x[/tex]
Upon substituting this value in equation (2), we will get:
[tex]2x+3(16-4x)=-2[/tex]
[tex]2x+48-12x=-2[/tex]
[tex]-10x+48=-2[/tex]
[tex]-10x+48-48=-2-48[/tex]
[tex]-10x=-50[/tex]
[tex]\frac{-10x}{-10}=\frac{-50}{-10}[/tex]
[tex]x=5[/tex]
Now, we will substitute [tex]x=5[/tex] in equation (1) to solve for y.
[tex]4*5+y=16[/tex]
[tex]20+y=16[/tex]
[tex]20-20+y=16-20[/tex]
[tex]y=-4[/tex]
Therefore, the solution for our given system would be [tex](5,-4)[/tex] and option B is the correct choice.
