Solve the simultaneous equation each part step wise The figure shown is a rhombu

Question

Solve the simultaneous equation each part step wise The figure shown is a rhombus its measurements are in cm. Calculate the length of a side. the perimeter the sides of the parallelogram are given in cm. Find x and y and parameter.

Explanation / Answer

z=2x+y+1 z=(3x-y-2)/2 z=x-y combining first and third equation: 2x+y+1=x-1 -> x+2y=-1 combining the second and third equation: (3x-y-2)/2=x-y -> 3x-y-2=2x-2y -> x+y=2 so now you have x+2y=-1 x+y=2 solve for one variable first, then the other: the second equation can be turned into x=2-y and substituted backinto the first equation: (2-y)+2y=-1 2+y=-1 y=-3 plug the y back into either of the equations (i'll use the secondone) x-3=2 ->x=5 so since x=5 and y=-3 and all sides are equal in length, then x-ygives the length of all sides x-y=5-(-3)=8cm the peremiter is the sum of the sides or 8+8+8+8=32cm ------------- x+y+1=3x-4 2y-x=x+2 -> -2x+y=-5 2y-2x=2 -> y-x=1 solving the first equation in terms of x gives y=2x-5 if you substitute that back into the second equation: (2x-5)-x=1 x-5=1 x=6, subsitite into the second equation again with x=6: y-x=1 ->y-6=1 -> y=7 x=6,y=7 the permiter is 2*one side + 2*other side 2(x+y+1) + 2(x+2) 2(6+7+1) + 2(6+2) 2*14 + 2*8 28+16 permiter = 44cm

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