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. (17, 20)

Explanation:

We have the following system of equations:

`x-3y=8` (1)

`5x-4y=5` (2)

Isolating
`x` from (1):

`x=(8+3y)/(4)` (3)

Substituting (3) in (2):

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

Isolating
`y`:

`(40)/(4)+(15 y)/(4)-4y=5` (5)

`10-5=4y-(15 y)/(4)` (6)

`y=20` (7)

Substituting (7) in (1):

`x-3(20)=8` (8)

Isolating
`x`:

`x=17` (9)

Hence, the correct option is d. (17, 20)