Question

Solve the system of equations algebraically.

4x – 3y = 8
5x - 4y = 5
a (16, 21)
b. many solutions
c. no solution
d. (17,20)

Answer 1

Answer: D

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=(5+4y)/(5)`

Now replace this in the first equation.

`4x-3y=8\\4((5+4y)/(5))-3y=8\\(20+16y)/(5)-3y=8`

Separate the terms.

`(20)/(5)+(16y)/(5)-3y=8`

Solve 20/5

`4+(16y)/(5)-3y=8`

Subtract 4 from both sides to isolate y.

`4-4+(16y)/(5)-3y=8-4`

`(16)/(5)y-3y=4`

Solve the difference.

`(16-(3)(5))/(5)y=4\\`

`(16-15)/(5) y=4`

`(1)/(5)y=4`

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

`((5)/(1) )((1)/(5))y=4((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=(85)/(5)\\x=17`