Answer: D
Step-by-step explanation:
[tex]4x-3y=8\\5x-4y=5[/tex]
Let's take one of the equations and solve for a variable to use the substitution method.
[tex]5x-4y=5\\5x=5+4y\\x=\frac{5+4y}{5}[/tex]
Now replace this in the first equation.
[tex]4x-3y=8\\4(\frac{5+4y}{5})-3y=8\\\frac{20+16y}{5}-3y=8[/tex]
Separate the terms.
[tex]\frac{20}{5}+\frac{16y}{5}-3y=8[/tex]
Solve 20/5
[tex]4+\frac{16y}{5}-3y=8[/tex]
Subtract 4 from both sides to isolate y.
[tex]4-4+\frac{16y}{5}-3y=8-4[/tex]
[tex]\frac{16}{5}y-3y=4[/tex]
Solve the difference.
[tex]\frac{16-(3)(5)}{5}y=4\\[/tex]
[tex]\frac{16-15}{5} y=4[/tex]
[tex]\frac{1}{5}y=4[/tex]
Multiply by the reciprocal or the inverted fraction that is next to y to isolate it.
[tex](\frac{5}{1} )(\frac{1}{5})y=4(\frac{5}{1})[/tex]
[tex]y=20[/tex]
Now, in order to find x, replace y in any of the two equations.
[tex]5x-4y=5\\5x-4(20)=5\\5x-80=5\\5x=5+80\\5x=85\\x=\frac{85}{5}\\x=17[/tex]
