Question

What values of a and y satisfy the system of equations 10x = 5y - 8 15x = -5y-2 Enter your answer as an ordered pair, like this: (42, 53) If your answer includes one or more fractions, use the /symbol to separate numerators and denominators. For example, if your answer is 42 64 53' 75 If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf." %), enter it like this: (42/53, 64/75)​

Answer 1

There are infinitely many solutions to this system.

We can solve the system of equations by elimination method:

10x = 5y - 8 (multiply both sides by 3)

15x = -5y - 2

30x = 15y - 24

15x = -5y - 2

Adding these two equations, we get:

45x = 13y - 26

Dividing both sides by 13, we get:

y = (45/13)x + 2

So any ordered pair (x, y) that satisfies this equation will also satisfy the system of equations given. There are infinitely many solutions to this system.

For example, if we let x = 13, then:

y = (45/13)(13) + 2 = 47

So one possible solution is (13, 47). Another possible solution is (26, 92/3).