Question

6x−3y=5 y−2x=8 ​ How many solutions does the system have?

Exactly one solution

No solutions

Infinitely many solutions

If your answer was Exactly one solution, what is this solution?

Answer 1

No Solutions because there are too many = signs.

Answer 2

no solution.

Explanation:

We have been given the system of equations

6x-3y=5...(i)

y-2x=8...(ii)

Write both equations in slope intercept form y = mx +b

For equation (i)

`6x-3y=5\\-3y=-6x+5\\\\y=2x-(5)/(3)`

The slope is 2 and the y- intercept is -5/3

For equation (ii)

`y-2x=8\\\\y=2x+8`

The slope is 2 and the y-intercept is 8

Since, both the equations have equal slope and different y - intercepts. Hence, the lines are parallel.

Therefore, we can say that the system have no solution.