# SOLUTION: 7X + 3Y = 14 , 5X + 9Y = 10 4X + Y = 16 , 2X + 3Y = 24 12X + Y = 25 , 8X - 2Y = 14

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: 7X + 3Y = 14 , 5X + 9Y = 10 4X + Y = 16 , 2X + 3Y = 24 12X + Y = 25 , 8X - 2Y = 14       Log On

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 Click here to see ALL problems on Linear-systems Question 174554: 7X + 3Y = 14 , 5X + 9Y = 10 4X + Y = 16 , 2X + 3Y = 24 12X + Y = 25 , 8X - 2Y = 14 Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website! ``` Notice the 3Y in the first equation and the 9Y in the second equation. If you multiply the first equation by -3, the 3Y will become -9Y and then if you add the two equations, the Y's will cancel. So let's multiply the first equation by -3: Simplifying: Now we add corresponding terms. -21X added to 5X gives -16X, -9Y added to 9Y gives 0, -42 added to 10 gives -32, so by adding vertically term by term we have the equation: Divide both sides by -16: Now pick either one of the original equations and substitute 2 for X: ----- Notice the 4X in the first equation and the 2X in the second equation. If you multiply the second equation by -2, the 2X will become -4X and then if you add the two equations, the X's will cancel. So let's multiply the second equation by -2: Simplifying: Now we add corresponding terms. 4X added to -4X gives 0, Y added to -6Y gives -5Y, 16 added to -48 gives -32, so by adding vertically term by term we have the equation: Divide both sides by -5: We could substitute this fraction in for Y as we did in the previous problem. However, unlike the previous problem, is difficult to subtitute. So instead we will start over: and this time we'll eliminate Y: Notice the Y in the first equation and the 3Y in the second equation. If you multiply the first equation by -3, the Y will become -3Y and then if you add the two equations, the Y's will cancel. So let's multiply the first equation by -3: Simplifying: Now we add corresponding terms. -12X added to 2X gives -10X, -3Y added to 3Y gives 0, -48 added to 24 gives -24, so by adding vertically term by term we have the equation: Divide both sides by -16: --- You do this one by yourself. It's just like the first one. Answer: , Edwin```