tell wheter the system has one solution, infinitely many solutions, or no solution:
y=3x-14
y-x=10
To determine whether the system of equations has one solution, infinitely many solutions, or no solution, we can solve the system using either the substitution method or the elimination method.
Let's solve the system using the elimination method:
Given equations:
1) y = 3x - 14
2) y - x = 10
First, let's re-arrange equation 2) to isolate the variable 'y':
y = x + 10
Now we have the system of equations:
1) y = 3x - 14
2) y = x + 10
Since both equations have 'y' isolated on one side, we can equate the right-hand sides of the equations to determine if they are equal:
3x - 14 = x + 10
Next, we solve the equation for 'x':
3x - x = 10 + 14
2x = 24
x = 12
Now substitute the value of 'x' back into either of the original equations (let's use equation 1)):
y = 3(12) - 14
y = 36 - 14
y = 22
Finally, we have found the values of 'x' and 'y', which are x = 12 and y = 22. The solution to the system is (x, y) = (12, 22).
Therefore, this system of equations has one solution.