Solve the system of equations using any method.
5x - 12y = 207
5x - 11y = 206
2007-07-12 08:20:46 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Subtract the second from the first equation:
5x-12y = 207
5x-11y = 206
-y = 1
y = -1
Substitute:
5x - 12(-1) = 207
5x + 12 = 207
5x = 195
x = 39
2007-07-12 08:26:21 · answer #1 · answered by Tony The Dad 3 · 1⤊ 0⤋
(1) 5x - 12y = 207
(2) 5x - 11y = 206
(ADDITION)
Subtract (1) from (2)
y= -1
multiply (1) by 11 giving
(3) 55x – 132y= 2277
Multiplhy (2) by 12 giving
(4) 60x -132y= 2472
Subtracting (3) from (4)
(5) 5x = 195
Solving for x…. multiplying both sides by 1/5,
x=39
Plug these values into the original two equations to check.
(DETERMINANTS)
A =
| 5 . . . -12 |
| 5 . . . -11 |
= (5)(-12)-(5)(-11)= -60 + 55 = -5
x=
| 207 . . -12 |
| 206 . . -11 |/A
= [(206)(-12)-(207)(-11)]/(-5) = (-2472 + 2277)/(-5) = (-195)/(-5) = 39
y=
| 5 . . 207 |
| 5 . . 206 |/A
=[(5)(207)-(5)(206)]/-5 = 5/(-5) = -1
You can use substitution too… but you get the same answer…
2007-07-12 08:45:10 · answer #2 · answered by gugliamo00 7 · 0⤊ 0⤋
5x - 12y = 207
- 5x + 11y = - 206----ADD
- y = 1
y = - 1
5x + 11 = 206
5x = 195
x = 39
x = 39 , y = - 1
2007-07-12 11:04:32 · answer #3 · answered by Como 7 · 0⤊ 0⤋
Subtract one problem from the other.
5x - 12y = 207
-5x - 11y = 206
____________
0x-1y=1
OR: y=1
2007-07-12 08:24:53 · answer #4 · answered by spunky&luvable 2 · 0⤊ 1⤋
use matrices if you have a grapher it will do it for you fast...
using [A]inv.[B] = [XY]
A is a 4X4 with the constants
[5 -12] INVERSE [207] [X]
[5 -11] [206] =[Y]
2007-07-12 08:27:50 · answer #5 · answered by Anonymous · 0⤊ 0⤋