Question

Determine whether the system of equations has one solution, no solution, or infinitely many solutions. 4x=10+4y and 2x-2y=15

Answer 1

infinitely many solutions

Explanation:

Given the simultaneous equation

4x=10+4y... 1

2x-2y=15 .... 2

_____________

4x-4y = 10 * 1

2x-2y = 15 * 2

__________--

4x-4y = 10

4x-4y = 30

Add both equation

8x - 8y = 10+30

8x-8y = 40

Divide though by 8

x-y = 5

x = 5 + y

Since the result gave 1 equation and 2 unknowns, then we will let x =k

k = 5 + y

y = k -5

k can be any integer

(x,y) = (k, k-5)

This show that the equation has infinitely many solutions