How To Solve Simple Bilinear Equations Under Extra Linear Constraints?

How do i solve these systems of equations?

• How do i solve these systems of equations? I don't get how to solve these ones becuase I can not get rid of x or y becuase they are not alined. So how do i solve them? Please show me step by step so i can lean how and plase don't plug the equations into a math website. I have a test on this tommmarow and I need to learn how to do these. Please show me step by step. Thanks!!!! -6x-5y=20 -y=6x+4 -3x+y=-2 -2=7x-y 3x= 5y-9 2y=3x+3 so how do i solve these? Thanks!

• Answer:

  You need to get at least either an x or y defined so you can get started on a problem. The first problem already has your y defined for you which is 6x + 4. So you need to substitute. 6x - 5(6x + 4) = 20 6x - 30x + 20 = 20 -24x = 0 x = 0 Then you take the x and substitute it in the other equation. y = 6(0) + 4. y = 4 4 = (0) + 4 (this is just to make sure the problem is correct). x = 0, y = 4 We just completed the first one. The second one takes a bit more work. Let's take an equation that takes the fewest steps to get a variable defined and get's easier. -3x + y = -2 Add 3x to both sides. y = -2 + 3x -2 = 7x +2 + 3x -2 = 10x + 2 -4 = 10x x = -0.4 3(-0.4) + y = -2 -1.2 + y = -2 y = -0.8 Let's go the third problem. Let's try the 2nd equation... you could try the 1st, but I'm doing the 2nd. 2y = 3x + 3 Divide everything by 2 y = 1.5x + 1.5 3x = 5 (1.5x + 1.5) - 9 3x = 7.5x + 7.5 - 9 3x = 7.5x - 1.5 -4.5x = -1.5 x = 3 2y = 3(3) + 3 2y = 9+3 2y = 12 y = 6 x = 3, y = 6 Ok I'll clear up your new question. The reason I divided everything by 2 is because the 2 and y are multiplying together. In order to seperate a multiplication expression, you need to divide both sides by the number that must go. Here's an example 2x = 6 We are trying to find what x equals. Divide both sides by 2. The 2 on the left side cancels since you are dividing by 2 on both sides, leaving you with x = 3 (2 divided by 2 is 1, 1 times x is x by itself). Plug back in. 2(3) = 6. It's true. That's why I divided on the 3rd problem.