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Olin [163]
3 years ago
12

Solve the system of equations algebraically.

Mathematics
1 answer:
nordsb [41]3 years ago
7 0

Answer: D

Step-by-step explanation:

4x-3y=8\\5x-4y=5

Let's take one of the equations and solve for a variable to use the substitution method.

5x-4y=5\\5x=5+4y\\x=\frac{5+4y}{5}

Now replace this in the first equation.

4x-3y=8\\4(\frac{5+4y}{5})-3y=8\\\frac{20+16y}{5}-3y=8

Separate the terms.

\frac{20}{5}+\frac{16y}{5}-3y=8

Solve 20/5

4+\frac{16y}{5}-3y=8

Subtract 4 from both sides to isolate y.

4-4+\frac{16y}{5}-3y=8-4

\frac{16}{5}y-3y=4

Solve the difference.

\frac{16-(3)(5)}{5}y=4\\

\frac{16-15}{5} y=4

\frac{1}{5}y=4

Multiply by the reciprocal or the inverted fraction that is next to y to isolate it.

(\frac{5}{1} )(\frac{1}{5})y=4(\frac{5}{1})

y=20

Now, in order to find x, replace y in any of the two equations.

5x-4y=5\\5x-4(20)=5\\5x-80=5\\5x=5+80\\5x=85\\x=\frac{85}{5}\\x=17

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