SOLUTION: {{{system(-10x - 11y + 7z = 145, 7x - 4y - 3z = 53, -5x - y = 146)}}} I need to solve this using any method. Id like to see the steps and the correct answer. I thi

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: {{{system(-10x - 11y + 7z = 145, 7x - 4y - 3z = 53, -5x - y = 146)}}} I need to solve this using any method. Id like to see the steps and the correct answer. I thi      Log On

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 Question 160537: I need to solve this using any method. Id like to see the steps and the correct answer. I think maybe I should start by multiplying the 3rd equation by 2 and then subtract it from the 1st equation? I'm trying to make sense of this but I just cant figure it out. I really appreciate your time. Thank you.Found 2 solutions by vleith, Edwin McCravy:Answer by vleith(2825)   (Show Source): You can put this solution on YOUR website!If you know matrices, you can use that. But I suspect you are not there yet. So, you might try substitution. I would start with equation 3. Use it to find y in terms of x You can then substitute that value for y into both equations 1 and 2. Simplify this to get an equation with just x and z in it Use it to find x in terms of z Simplify this one too and get an equation with just x and z. Substitute the z value in this last equation with the "z in terms of x" from the earlier equation. You now have one equation with only x and constants in it. Solve for x. Niw use this value of x and the equation with z in terms of x to find z. Then use x and z in any of the equations to solve for y (I would use the third original equation since it has only x and y in it) Answer by Edwin McCravy(8908)   (Show Source): You can put this solution on YOUR website!Edwin's solution: ``` That would work, but it would be the best way. First you should observe that z is already eliminated from the third equation, so you should eliminate z from the first two equations: To eliminate z from the first two equations: Multiply the first equation by 3 and the second equation by 7, then add them: 3[-10x - 11y + 7z = 145] 7[ 7x - 4y - 3z = 53] -30x - 33y + 21z = 435 49x - 28y - 21z = 371 19x - 61y = 806 Now we take the third original equation with this equation and solve this system: We can do this by substitution: Solve the first equation for y: Substitute for in Substitute that into Now substitute and into either one of the first two original equations. Edwin```