<span>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 </span>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.<span> 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 </span>In this case we are not able to delete any of the variables so we multiplied by -1 to be able to eliminate x. <span> Then to find x we substitute the value of y in any of the formulas.</span><span><span> </span>4x-2=10<span> 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 </span></span>In this case we are not able to delete any of the variables so we multiplied by 3 to be able to eliminate y. <span> Then to find y we substitute the value of x in any of the formulas.</span> <span> 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. <span> Then to find y we substitute the value of x in any of the formulas.</span> 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</span>
