To determine how many solutions this linear system has, we can solve the equations.
The first equation is:
y = x + 2
Now, we can substitute this expression for y into the second equation:
6x – 4(x + 2) = 10
Expanding this gives:
6x – 4x – 8 = 10
Combining like terms:
2x – 8 = 10
Now, we add 8 to both sides:
2x = 18
Dividing both sides by 2:
x = 9
Now substituting back to find y:
y = 9 + 2 = 11
This gives us a single solution: (9, 11).
Since we found one unique solution, we can conclude that this linear system has exactly one solution.