Answer:
Step-by-step explanation:
I used Cramer's Rule to find y, since we can isolate and solve for individual variables using Cramer's Rule. Do that by finding the determinant of the matrix, |A|. The matrix A looks like this:
2 -2 1
-1 3 2
1 -4 -3
and we find the determinant of a 3x3 by expanding it. Do that by picking up the first 2 columns and throw them on at the end, like this:
2 -2 1 2 -2
-1 3 2 -1 3
1 -4 -3 1 -4
and find the determinant by multiplying along the 3 major axes and subtract from that the product of the 3 minor axes:
[(2*3*-3)+(-2*2*1)+(1*-1*-4)] - [(1*3*1)+(-4*2*2)+(-3*-1*-2)] which simplifies to
-18 - (-19) = 1
So the determinant of the matrix A is |A| = 1.
Now to find the determinant of Ay, we replace the y column with the solutions and so the same thing by expansion and then multiplying and subtracting:
2 -7 1 2 -7
-1 0 2 -1 0
1 1 -3 1 1
and find the determinant of y:
[(2*0*-3)+(-7*2*1)+(1*-1*1)] - [(1*0*1)+(1*2*2)+(-3*-1*-7)] which simplifies to
-15 - (-17) = 2
So the detminant of y is |Ay| = 2
We can solve for the variable now by dividing Ay by A:
2 / 1 = 2
So the solution for y = 2
