17
3x - 6y = 9, 5x + 4y = -27 6x - 12y = 18, 15x + 12y = -81 21x = -63 x = -3 (3 x -3) = 9 + 6y (-9 - 9)/6 = y y = -3 Check: (5 x -3) + (4 x -3) = -15 -12 = -27 QED
If: y = 5x and y = 3 -x Then: 5x = 3 -x => 5x +x = 3 => 6x = 3 => x = 1/2 By substitution point of contact is at: (1/2, 5/2)
x=2 y=7 5x+3y= 5 7 x 2 x 3 ____ _____ 10 21 21 + 10 _______ 31
y = 11
5x=4012y=84124
10 z's.
17
3x - 6y = 9, 5x + 4y = -27 6x - 12y = 18, 15x + 12y = -81 21x = -63 x = -3 (3 x -3) = 9 + 6y (-9 - 9)/6 = y y = -3 Check: (5 x -3) + (4 x -3) = -15 -12 = -27 QED
If y equals 5x-15 and x equals 1 then the value of y comes out to be -10. So y equals 5x-15 is -10.
-5x + y = -12- 3x + 6y = -12Since both of expressions have a value of -12, their sum is - 24. This is true only whenx = 20/9 and y = -8/9.-5x + y = -12y = 5x - 12- 3x + 6y = -12-3x + 6(5x - 12) = -12-3x + 30x - 72 = -1227x = 60x = 60/27x = 20/9y = 5x - 12y = 5(20/9) - 12y = 100/9 - 12y = (100 - 108)/9y = -8/9
Add: 5x - y + x + y + 8 + 10 ie 6x = 18 so x = 3 and y = 7
5x - 3y = 23 7x - 4y = 33 multiply 1st eq by 4 and second by 3: 20x - 12y = 92 21x -12y = 99 Now subtract equations: -x = -7 x = 7 substitute x into either equation: 5(7) - 3y = 23 35 - 3y = 23 -3y = -12 y = 4
5x -3y = 23 7x - 4y = 33 This is simultanreous equations. Arbitrarily decide which letter to eliminate. In this case 'y' To do this multiply the top eq'n by '-4' and the bottom by '3' Hence -20x + 12y = -92 21x - 12y = 99 Add the two eq'ns. This will eliminate 'y' x = 7 Substitute into either eq'n for 'y' 49 - 4y = 33 -4y = - 16 y = 4 Hence (x,y) = ( 7,4)
x=6 y=30
If: y = 5x and y = 3 -x Then: 5x = 3 -x => 5x +x = 3 => 6x = 3 => x = 1/2 By substitution point of contact is at: (1/2, 5/2)
-30