3x+2y=20 5x-2y=1 (3x+2y) + (5x-2y)= 20+1 3x+5x= 21....... 8x=21.........x=2 5/8 Subsitute x=3(2 5/8)+ 2y=20........... 7 7/8 +2y=20.........2y= 20- 7 7/8....... y=6 1/16
(3, -4)
If: 3x+2y = 5x+2y = 7 which is the same as 7 = 7 = 7 Then: 3x+2y = 7 and 5x+2y = 7 Subtracting equations: x = 0 Therefore by substitution: x = 0 and y = 3.5
If: 3x+2y = 5x+2y = 7 Then: 3x+2y = 7 and 5x+2y = 7 Subtract the 1st equation from the 2nd equation: 2x = 0 or x = o By substitution: x = 0 and y = 3.5
x = 3, y = -4
3x+2y=20 5x-2y=1 (3x+2y) + (5x-2y)= 20+1 3x+5x= 21....... 8x=21.........x=2 5/8 Subsitute x=3(2 5/8)+ 2y=20........... 7 7/8 +2y=20.........2y= 20- 7 7/8....... y=6 1/16
(3, -4)
If: 3x+2y = 5x+2y = 7 which is the same as 7 = 7 = 7 Then: 3x+2y = 7 and 5x+2y = 7 Subtracting equations: x = 0 Therefore by substitution: x = 0 and y = 3.5
If: 3x+2y = 5x+2y = 7 Then: 3x+2y = 7 and 5x+2y = 7 Subtract the 1st equation from the 2nd equation: 2x = 0 or x = o By substitution: x = 0 and y = 3.5
x = 3, y = -4
x = 3 and y = -4
2y - x = 3 y = -5x + 7 Rewrite the second y + 5x = 7 Mutiply it by 2 2y + 10x = 14 Now subtract the first equation from this: 2y + 10x = 14 2y - x = 3 11x = 11 Divide both sides by 11: x = 1 Substitute for x in the first equation: 2y - 1 = 3 Add 1 to both sides: 2y = 4 Divide both sides by 2: y = 2 Answer: (x, y) = (1, 2)
5x + 2y = 4 (Eq1) -5x + 2y = -10 (Eq2) Add the two equations 4y = -6 so y = -1.5 x = (4 - (2 x -1.5))/5 = (4 + 3)/5 = 7/5 = 1.4 Check: 5 x 1.4 + 2 x -1.5 = 7 - 3 = 4; -5 x 1.4 + 2 x - 1.5 = -7 - 3 = -10 QED
If: 3x+2y = 5x+2y = 14 Then: 3x+2y = 14 and 5x+2y =14 Subtract the 1st equation from the 2nd equation: 2x = 0 Therefore by substitution the solutions are: x = 0 and y = 7
7
-3x + y = 7 5x + 2y = 3 This is solved by SIMULTANEOUS Eq'ns. Arbitrarily decide which letter to eliminate. In this case 'y' . To do this multiply the top eq'n by '-2' Hence (+)6x - 2y = -14 ( Notice the double negative multiple becomes plus(+). 5x + 2y = 3 Add the two eq'ns 11x = -11 (Notice the 'y' has been eliminated). x = -1 When x = -1 -3(-1) + y = 7 3 + y = 7 y = 4 Hence the solution in ( x,y) form is ( -1,4).
3x + 2y = 5x + 2y = 7Subtract (2) from (1) to give: 3x - x + 2y - 2y = 5 - 7→ 2x = -2→ x = -1Substitute for x in (1)3(-1) + 2y = 5→ -3 + 2y = 5→ 2y = 8→ y = 4Substitute for x and y in (2) to check answer:x + 2y = -1 +2(4) = -1 + 8 = 7 as required. Thus:x = -1y = 4