Find the coordinates of the intersection point that sells the system of these two linear equations in two variables 2X plus Y equals 15 and Y equals negative X +5
To find the intersection point that satisfies both equations, we need to solve the system of equations.
Let's first rewrite the equations in the standard form:
2X + Y = 15 ...(1)
Y = -X + 5 ...(2)
We can now solve the system using substitution or elimination method.
Substituting equation (2) into equation (1), we get:
2X + (-X + 5) = 15
2X - X + 5 = 15
X + 5 = 15
X = 15 - 5
X = 10
Now, substitute the value of X back into equation (2):
Y = -X + 5
Y = -10 + 5
Y = -5
Therefore, the intersection point is (10, -5).
To find the coordinates of the intersection point of the system of these two linear equations, we can solve the equations simultaneously.
Step 1: Start with the given equations:
2X + Y = 15 ...(Equation 1)
Y = -X + 5 ...(Equation 2)
Step 2: Substitute Equation 2 into Equation 1 to eliminate Y:
2X + (-X + 5) = 15
Simplifying the equation, we have:
X + 5 = 15
Step 3: Solve for X:
X + 5 - 5 = 15 - 5
X = 10
Step 4: Substitute the value of X back into Equation 2 to solve for Y:
Y = -X + 5
Y = -(10) + 5
Y = -10 + 5
Y = -5
Step 5: The solution to the system of equations is X = 10 and Y = -5.
Therefore, the intersection point of the two lines is (10, -5).
To find the coordinates of the intersection point, we need to solve the system of equations:
Equation 1: 2X + Y = 15
Equation 2: Y = -X + 5
We can solve this system of equations using the method of substitution or elimination. Let's use the method of substitution in this case.
In Equation 2, we have Y = -X + 5. We can substitute this value of Y in Equation 1:
2X + (-X + 5) = 15
Simplifying the equation, we get:
2X - X + 5 = 15
X + 5 = 15
X = 15 - 5
X = 10
Now that we have the value of X, we can substitute it back into either Equation 1 or Equation 2 to find the value of Y. Let's substitute it back into Equation 2:
Y = -X + 5
Y = -10 + 5
Y = -5
Therefore, the coordinates of the intersection point are (10, -5).