To find the x-coordinate of point P, we need to solve the following system of equations:
6x - 3y = 36
-2x + 7y = 12
We can solve this system of equations by using the method of elimination. Let's first multiply the first equation by 2 and the second equation by 3 to make the coefficients of x the same:
12x - 6y = 72
-6x + 21y = 36
Now, add these two equations:
12x - 6y - 6x + 21y = 72 + 36
6x + 15y = 108
2x + 5y = 36
Now, we can solve this equation for x by isolating x:
2x + 5y = 36
2x = 36 - 5y
x = (36 - 5y) / 2
Since we know the image of point P under the transformation T is (36, 12), we can substitute these values into the equation x = (36 - 5y) / 2:
36 = (36 - 5y) / 2
72 = 36 - 5y
5y = -36
y = -7.2
Now, substitute this value of y back into the equation x = (36 - 5y) / 2:
x = (36 - 5(-7.2)) / 2
x = (36 + 36) / 2
x = 72 / 2
x = 36
Therefore, the x-coordinate of point P is 36.
Transformation T is defined by T (x, y) = [ 6 -3 -2 7 ][ x y ].
In the xy-plane, the image of point P under the transformation T is (36, 12). What is the x-coordinate of point P?
1 answer