Determine the number of solutions to the system of linear equation 2X plus Y equals 64X plus 2Y equals eight
To determine the number of solutions, we need to find the intersection point of the two lines represented by the equations.
First, let's rewrite the system of equations in standard form:
2X + Y = 64
64X + 2Y = 8
To eliminate the Y variable, let's multiply the first equation by 2 and the second equation by -1:
4X + 2Y = 128
-64X - 2Y = -8
Now, let's add the two equations together to eliminate the Y variable:
4X + (-64X) + 2Y + (-2Y) = 128 + (-8)
-60X = 120
X = -2
Now that we have found the value of X, we can substitute it back into the first equation to find the value of Y:
2(-2) + Y = 64
-4 + Y = 64
Y = 68
Therefore, the system of equations has a unique solution at X = -2 and Y = 68. Thus, the number of solutions to the system of equations is one.