describe and correct the error in solving the system linear of equations.
-4x+y=4
4x+y=12
it has a graph and it says " The lines do not intersect, So, the system has no solutions"
clearly the lines have different slopes, so they must intersect.
To solve the system of linear equations:
-4x + y = 4 ...(Equation 1)
4x + y = 12 ...(Equation 2)
You have correctly identified that the lines do not intersect, indicating that there is no solution to the system. This can also be verified algebraically by solving the equations.
To correct the error in solving the system, let's check for any mistakes made during the process:
Step 1: Add the equations
(-4x + y) + (4x + y) = 4 + 12
Simplifying:
-4x + 4x + y + y = 4 + 12
0x + 2y = 16
2y = 16
Here lies the error. By adding the equations, both the x terms cancel each other (-4x + 4x = 0x), leaving us with 2y = 16. However, this equation does not provide any information about the value of y or x.
In a correct process, we should follow the elimination method to eliminate one of the variables:
Step 1: Multiply Equation 1 by 1 and Equation 2 by -1 to eliminate the x terms.
-4x + y = 4 ...(Equation 1)
-4x - y = -12 ...(Equation 2)
Step 2: Add the equations
(-4x + y) + (-4x - y) = 4 - 12
Simplifying:
-8x = -8
Dividing both sides by -8:
x = 1
Step 3: Substitute the value of x into either Equation 1 or Equation 2 to solve for y.
Using Equation 1:
-4(1) + y = 4
-4 + 4 = y
0 = y
So, the solution to the system of equations is x = 1 and y = 0. In this case, the lines are parallel, indicating that they do not intersect.