Review the grass of a system of two linear equations in two variables Y equals X minus XNY equals negative X +4 find solution of both equations what is the intersection point

Question

Review the grass of a system of two linear equations in two variables Y equals X minus XNY equals negative X +4 find solution of both equations what is the intersection point

Answer 1

To find the solution of both equations and the intersection point, let's first write the system of equations:

Equation 1: Y = X - XN
Equation 2: Y = -X + 4

Now, let's set the two equations equal to each other to find the intersection point:

X - XN = -X + 4

Simplifying the equation by adding X to both sides:

2X - XN = 4

Factoring out X:

X(2 - N) = 4

To find the value of X, we need to consider two cases:

1. Case 1: When (2 - N) is not equal to zero
If (2 - N) is not equal to zero, we can divide both sides of the equation by (2 - N) to solve for X:

X = 4 / (2 - N)

2. Case 2: When (2 - N) is equal to zero
If (2 - N) is equal to zero, we cannot divide by zero. In this case, there is no unique solution for X.

Now, let's calculate the corresponding value of Y:

For Equation 1: Y = X - XN
Substituting the value of X into Equation 1, we get:

Y = (4 / (2 - N)) - (4 / (2 - N)) * N
Simplifying further:

Y = (4 / (2 - N)) - (4N / (2 - N))
Y = (4 - 4N) / (2 - N)

Hence, the solution of the system of equations is given by the values of X and Y obtained for each case:

1. If (2 - N) is not equal to zero:
Intersection Point: (X, Y) = (4 / (2 - N), (4 - 4N) / (2 - N))

2. If (2 - N) is equal to zero:
No unique solution for X and Y.

Answer 2

To find the intersection point of the system of two linear equations, we can solve the equations simultaneously. Let's start with the given equations:

Equation 1: Y = X - XN
Equation 2: Y = -X + 4

To find the intersection point, we need to equate the values of Y in both equations:

X - XN = -X + 4

Now, let's solve this equation step-by-step:

Step 1: Combine like terms:

2X + XN = 4

Step 2: Factor out the common factor, which is X:

X(2 + N) = 4

Step 3: Divide both sides of the equation by (2 + N):

X = 4 / (2 + N)

The value of X is now expressed in terms of the variable N.

To find the value of Y, substitute the value of X into either of the original equations. Let's use Equation 1:

Y = X - XN

Substituting X = 4 / (2 + N):

Y = (4 / (2 + N)) - (4N / (2 + N))

To simplify further, we can find the common denominator:

Y = (4 - 4N) / (2 + N)

Now we have the value of Y in terms of N.

Therefore, the solution of the system of equations is:

X = 4 / (2 + N)
Y = (4 - 4N) / (2 + N)

This represents the intersection point of the two equations.

Answer 3

To find the intersection point of the system of two linear equations, we need to solve the equations simultaneously. Let's solve the equations step by step.

The system of equations is:
Y = X - XN
Y = -X + 4

Step 1: Set the two equations equal to each other:
X - XN = -X + 4

Step 2: Simplify the equation by grouping like terms:
X + X = 4

Step 3: Combine like terms:
2X = 4

Step 4: Solve for X by dividing both sides of the equation by 2:
X = 2

Step 5: Substitute the value of X (2) back into one of the original equations to find the value of Y:
Y = X - XN
Y = 2 - (2N)

Step 6: Simplify the equation by combining terms:
Y = 2 - 2N

So, the solution to the system of equations is the point (2, 2 - 2N), where N can be any real number.

The intersection point of the two equations is (2, 2 - 2N).