Mathematics
kris1010
42

Use the elimination method 1) 3x+y=-1 5x-y=9 2) 4x+6y=24 4x-y=10 3)2x-y=-3 x+3y=16 4) 2x+3y=7 3x+4y=10

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(1) Answers
phair

1) 3x+y=-1 5x-y=9     First of all we have add both equation but to be sure that the value we want to eliminate are both in a way that would make it possible t be deleted.     3x+y=-1      5x-y= 9     8x = 8       x= 1 In this case we are able to eliminate y becuase if we add +y-y we get that our answer is 0. and 3x + 5x would be 8x and -1+9 would be equal to 8 and to find x we needed to divided giving us that the answer for x is 1 becuase 8/8 is 1. Then to find y we substitude the value of x in any of the formulas. 3(1)+y= -1  3+y= -1  y= -1-3  y=-4 When we have our y value we can determine if it is correct by replace the values. 5(1)--4= 9 5+4= 9 9=9 Up until now we are fine. So we do the same with the other equation. 3(1)+-4=-1 3+-4=-1 -1=-1  So by this we can now detemine that. x= 1 y= -4 2) 4x+6y=24 4x-y=10  4x+ 6y =24     4x-y=10 (*-1)     4x+6y=24     -4x+y=-10     7y= 14      y= 14/7      y= 2 In this case we are not able to delete any of the variables so we multiplied by -1 to be able to eliminate x.  Then to find x we substitute the value of y in any of the formulas.      4x-2=10       4x= 10+2      x= 12/4       x= 3 So we now know our variables so we substituted them to see if they are correct.       4(3)+6(2)=24        12+12=24        24=24 We do the same with the other equation.       4(3)-2=10       12-2 =10        10= 10 So we can assume that.               x= 3        y= 2 3)2x-y=-3 x+3y=16   (3*)2x- y= -3      x+ 3y = 16    6x -3y = -9     x+3y =16    7x= 7    x= 1 In this case we are not able to delete any of the variables so we multiplied by 3 to be able to eliminate y.  Then to find y we substitute the value of x in any of the formulas.     1+ 3y = 16  3y= 16-1  y= 15/3  y= 5  So we now know our variables so we substituted them to see if they are correct. 2(1)- 5 =-3 2-5= -3 -3= -3 We do the same with the other equation. 1+3(5)= 16 1+15=16 16=16 So we now are sure that x= 1 y= 5 4) 2x+3y=7 3x+4y=10 2x+3y =7 ( * - 4) 3x+4y =10 ( * 3) -8x -12y = -28 9x +12y = 30 x= 2 In this case we are not able to delete any of the variables so we multiplied one of teh quations by - 4 to be able to subtract in our sum and the other by 3 to have the same number on y to be able to eliminate y.  Then to find y we substitute the value of x in any of the formulas. 2(2)+3y= 7 4+3y=7 3y= 7-4 y= 3/3 y= 1 So we now know our variables so we substituted them to see if they are correct. 3(2)+4(1)= 10 6+4=10 10=10 We do the same for the other 2(2)+3(1)=7 4+3= 7 7=7 So with that we can say that. x= 2 y= 1

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