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Worked solution of problem similar to M1 3X – 5y = 13 4X + 8y = 7 The trick to solve these is you need to add or subtract one entire equation from the other one to eliminate one of the unknowns. You can eliminate either X or Y first. I am going to chose to eliminate X first. With my experience I know I will have smaller number s to deal with if I do. To eliminate X I first recognise that the lowest common multiple of 4 and 3 is 12. So I’ll multiply the entire first equation by 4 and the entire second equation by 3. 4 x( 3X-5y = 13) is the same as 12X-20y =52 3 x (4X + 8y = 7) is the same as 12X +24y =21 Now we need to decide if we are adding the equations or subtracting them. In this case I can see that I need to subtract the second one from the first one to eliminate X altogether 12X – 20y = 52 -( 12X +24y =21 ) 12X-12X = 0 First equation 12X Minus second equation 12X Yields new equation 12X-12X =0X =0 with no “X” therefore -20y-24y =-44y 52-21 =31 -20y 24y 20y-24y =-44y =52 =21 =52-21 =31 -44y =31 Thus -44y = 31 (then multiply both sides of equation by -1) So 44y = -31 (Then divide both sides of the equation by 44) So y =-31/44 = 0.704545 (exactly or 0.70 if the answer is to an engineering question that might only requires accuracy of about +/- 1%. In this case none of the numbers in the problem are expressed to more than 2 significant figures so it is completely fictitious accuracy to express the answer to more than three significant figures) Anyway to work out x is we need to substitute the value of y back into one of the original equations. 3x – 5y = 13 4x + 8y = 7 I am choosing the second one because 8 and 44 have a common factor but it really doesn’t matter So 4X + 8(-31/44) = 7 So 4X + 4(-31/22) = 7 this is a bit of simplification that someone without a calculator might bother to do! So 4X + 2(-31/11) = 7 this is a further bit of simplification that someone without a calculator might do! So 4X -62/11 = 7 now we need to add 62/11 to both sides to yield 4X -62/11 +62/11 = 7 + 62/11 4X = 7+62/11 now because I don’t like relying on a calculator a writing down really long numbers and worrying about precision I would express this as follows the trick here is that 7=77/11. I do this so I can easily add the whole number to the fraction to yield a fraction. 4X = 77/11 + 62/11 =( 77+62)/11 = 139/11 (now we are ready to divide both sides of the equation by 4X/4 = (139/11)/4 X = 139/44 Now we really need the calculator unless we want to practice long division X = 3.159091 (exactly or I would probably express it as 3.16 if this was a final number that was needed to an engineering problem when none of the original numbers were given to more than 2 significant figures) Merit 1 will be achieved by exam so I recommend getting plenty of practice Here are some for you to solve M1 (a) 8X - 8Y = 20 2X + 4Y = 4 M1(b) 3X + 5Y = 12 6X – 10Y = 16 If you want more to solve please ask. Any pair of equations like this has a solution. If you can find a pair of equations like this that has no solution then let me know. The only example I can think of is if you write two equations for two parallel lines (these will never intersect at any x,y spot on a graph.)