Question

How many unique solutions are there to the system of equations below?

2x-y=6
3x+5y=-17

A. zero
B. one
C. two
D. infinite

Answer 1

Hello!

`\large\boxed{B. \text{ } One}`

2x - y = 6

3x + 5y = -17

Solve systems of equations by elimination.

The easiest variable to eliminate would be y since we can simply multiply the first equation by 5:

5(2x - y = 6)

3x + 5y = -17

10x - 5y = 30

3x + 5y = -17

Eliminate y by adding both equations to each other:

10x - 5y = 30

3x + 5y = -17

-------------------

13x + 0y = 13

13x = 13

13x/13 = 13/13

x = 1

Therefore, there is only ONE solution to this system of equations because we only could derive one solution.