How To Solve Simple Bilinear Equations Under Extra Linear Constraints?

Solve the systems of Equations?? and Cramers Rule Please Help?

• Solve the systems of Equations?? and Cramers Rule Please Help? Solve the systems of Equations? 4a-12b =2 (1) 8a+80c=80 (2) 24b+64c=62(3) I got it wrong on the test the answer is (5/4, 1/4,7/8) but please help me learn how they got the answer with steps. Also this one with Cramers Rule! x-4y=14 4y+z=2 -x+z=-2 Also got this one wrong the answer is 9,-5/4, 7 but how did it come out to be this answer please help! This one I was not sure how to solve! 8x-x+z=-31 2x+2y-3z+-15 x-3y+2z=-6 How do I solve this problem will it be Cramers Rule also! Thanks and Appreciated

• Answer:

  I've given a source for Cramer's Rule below. This is a trivial look-up on line, with plenty of hits and examples. I'm not sure whether you have to use Cramer's Rule for all of these, since your English skills need attention, too. However, let's do the first one with more direct manipulation. First of all, we divide each equation by the common constants: 2a - 6b = 1 1a + 10c = 10 12b + 32c = 31 Solve the second equation for a: a = 10 - 10c Substitute into the first: 20 - 20c - 6b = 1 6b + 20c = 19 12b + 40c = 38 Subtract the second equation from this: 8c = 7 c = 7/8 The other two values follow immediately from there. --------------------------- Now, let's look at the solution with Cramer's Rule. First, the equations with zero coefficients filled in for the missing variables: 2a - 6b + 0c = 1 1a + 0b + 10c = 10 0a + 12b + 32c = 31 To find the value of a, plug in the right-hand sides for the a column in your 3x3 matrix, and divide the discriminants: | 2 -6 0 | | 1 0 10| |0 12 32| ------------- | 1 -6 0 | |10 0 10 | |31 12 32| This division should give you 5/4; I'm assuming that you're already comfortable with (although tired of) doing discriminants, so I won't bore Y!A with the arithmetic. Finding the value of b works similarly, substituting into the middle column: | 2 1 0 | | 1 10 10| |0 31 32| ------------ | 2 -6 0 | | 1 0 10| |0 12 32| See how it works? Can you finish from here?