Question

Question content area top
Part 1
Without graphing the​ equations, decide whether the system has one​ solution, no​ solution, or infinitely many solutions.
3 y equals x minus 8
4 x minus 6 y equals 16
Question content area bottom
Part 1
How many solutions does the system​ have?
One solution
Infinitely many solutions
No solution

Answer 1

One solution.

Solve: from 3y = x − 8, x = 3y + 8. Substitute into 4x − 6y = 16:
4(3y + 8) − 6y = 16 → 12y + 32 − 6y = 16 → 6y = −16 → y = −8/3, x = 0.
So the lines intersect at (0, −8/3).