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

Question

asked Jan 7, 2021 13.4k views

1 Answer

Jacxel · Answer 1 · 2021-01-11T02:42:44+0000

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.

$5x-4y=5\\5x-4(20)=5\\5x-80=5\\5x=5+80\\5x=85\\x=(85)/(5)\\x=17$