Tell whether the linear system has ONE SOLUTION, NO SOLUTION, or INFINITELY MANY SOLUTIONS.
4x-y=2
-x+3y=9
y = 4 x - 2
y = (1/3)x + 3
The lines are not parallel.
There is one solution
Since the slopes of the two lines are different , you are intersecting two non-parallel lines.
In how many points to they intersect?
Thank you..
To determine whether the linear system has one solution, no solution, or infinitely many solutions, we can solve the system of equations using the method of elimination or substitution.
Method of elimination:
First, let's multiply the second equation by 4 to make the coefficients of x in both equations the same:
4x - y = 2
-4x + 12y = 36
Next, add the two equations together to eliminate x:
(4x - y) + (-4x + 12y) = 2 + 36
-1y + 11y = 38
10y = 38
y = 3.8
Now, substitute the value of y back into one of the original equations to find the value of x:
4x - (3.8) = 2
4x - 3.8 = 2
4x = 2 + 3.8
4x = 5.8
x = 1.45
Therefore, the solution to the linear system is x = 1.45 and y = 3.8. As there is a unique solution, this means the linear system has ONE SOLUTION.