Find all solutions to these problems
2007-09-11 05:33:24 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x + 3y = 4
-x + 2y = 11----ADD
5y = 15
y = 3
x + 9 = 4
x = - 5
x = - 5 , y = 3
2007-09-15 00:06:05 · answer #1 · answered by Como 7 · 0⤊ 0⤋
If x/3 + y = 4/3, then x + 3y = 4. As a result, we know x + 3y = 4 and -x + 2y = 11. If you add these two equations together to cancel out x, you get:
x + 3y = 4
-x + 2y = 11
----------------
5y = 15
y = 3.
And as a result, x + (3*3) = 4, or x + 9 = 4, or x = -5.
2007-09-11 12:41:30 · answer #2 · answered by RustyL71 4 · 0⤊ 0⤋
All solutions that will work for both problems, or all solutions that will work for each problem?
For example, (x=4, y=0) will work for the 1st. So will (x=7, y=1), (x=10, y=2), (x=14, y=3), just to start
For the second one, (x=1, y=6), (x=3, y=7), etc.
If you want all solutions that work for both, you're looking for a much smaller set of numbers.
Solve one for "y".
-x +2y = 11
2y = 11 + x
y = 5.5 + .5x
Sub it in for the other "y"
x/3 + y = 4/3
x/3 + (11/2) + x/2 = 4/3
Multiply everything by 6 (lowest common denominator)
2x + 33 + 3x = 8
Simplify
5x = -25
x = -5
Now that you have x, sub it in and solve for "y"
2007-09-11 12:47:48 · answer #3 · answered by saberhilt 4 · 0⤊ 0⤋
x/3+y=4/3 can be written
x+3y=4
-x+2y=11
add the two equations
5y=15 so y=3
substitute in either equation for y
-x+6=11
-x=11-6=5
x=-5
2007-09-11 12:43:24 · answer #4 · answered by frozen 5 · 0⤊ 0⤋
Find value of y:
x/3 + y = 4/3
y = 4/3 - x/3
Find value of x:
- x + 2(4/3 - x/3) = 11
- x + 8/3 - 2/3x = 11
- 3/3x - 2/3x = 33/3 - 8/3
- 5/3x = 25/3
x = - 5
Derived value of y with x as - 5:
y = 4/3 - (- 5/3)
y = 4/3 + 5/3
y = 3
Answer: x = - 5, y = 3
Proof:
- 5/3 + 3 = 4/3
- 5/3 + 9/3 = 4/3
- (- 5) + 2(3) = 11
5 + 6 = 11
2007-09-11 12:55:05 · answer #5 · answered by Jun Agruda 7 · 3⤊ 0⤋
x+3y=4 (multiply equation 1 by 3) --- (1)
-x+2y=11 --- (2)
add (1) and (2)
5y=15
y=3
(2) becomes
-x+2(3)=11
-x+6=11
-x=5
x=-5
x=-5 y=3
check : -x+2y=-(-5)+2(3)=5+6=11
2007-09-11 12:43:16 · answer #6 · answered by cidyah 7 · 0⤊ 0⤋
x/3+y = 4/3 ..........(1)
-x+2y = 11 .........(2)
(1) x 3 >> x+3y = 4 ......(3)
(2)+(3) >> 5y = 15
y = 3
Substituting the value of y in (2), we get
-x+6 = 11
-x = 11-6 = 5
x = -5
y = 3
2007-09-11 12:44:17 · answer #7 · answered by Eechhutti 2 · 0⤊ 0⤋
x/3 + y = 4/3 => x + 3y = 4
-x + 2y = 11
Add them
5y = 15
y = 3
From this, we know x = -5
2007-09-11 12:40:57 · answer #8 · answered by PMP 5 · 1⤊ 0⤋